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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 307230.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 307230.c1 | 307230c8 | \([1, 1, 0, -1049789843, -13003763088147]\) | \(1087533321226184807035053481/8484255812957933638080\) | \(998164212138687934586473920\) | \([2]\) | \(222953472\) | \(4.0092\) | |
| 307230.c2 | 307230c5 | \([1, 1, 0, -1047816368, -13055406686412]\) | \(1081411559614045490773061881/522522049500\) | \(61474196601625500\) | \([2]\) | \(74317824\) | \(3.4599\) | |
| 307230.c3 | 307230c6 | \([1, 1, 0, -110636243, 111141274413]\) | \(1272998045160051207059881/691293848290254950400\) | \(81330029957500204659609600\) | \([2, 2]\) | \(111476736\) | \(3.6626\) | |
| 307230.c4 | 307230c3 | \([1, 1, 0, -85548243, 304133223213]\) | \(588530213343917460371881/861551575695360000\) | \(101360681328983408640000\) | \([2]\) | \(55738368\) | \(3.3161\) | |
| 307230.c5 | 307230c2 | \([1, 1, 0, -65488868, -204008934912]\) | \(264020672568758737421881/5803468580250000\) | \(682772274997832250000\) | \([2, 2]\) | \(37158912\) | \(3.1133\) | |
| 307230.c6 | 307230c4 | \([1, 1, 0, -63161368, -219178183412]\) | \(-236859095231405581781881/39282983014374049500\) | \(-4621603668658092549625500\) | \([2]\) | \(74317824\) | \(3.4599\) | |
| 307230.c7 | 307230c1 | \([1, 1, 0, -4238868, -2949684912]\) | \(71595431380957421881/9522562500000000\) | \(1120319955562500000000\) | \([2]\) | \(18579456\) | \(2.7667\) | \(\Gamma_0(N)\)-optimal |
| 307230.c8 | 307230c7 | \([1, 1, 0, 427109357, 875062673773]\) | \(73240740785321709623685719/45195275784938365817280\) | \(-5317179000822213800037174720\) | \([2]\) | \(222953472\) | \(4.0092\) |
Rank
sage: E.rank()
The elliptic curves in class 307230.c have rank \(0\).
Complex multiplication
The elliptic curves in class 307230.c do not have complex multiplication.Modular form 307230.2.a.c
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
