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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 14400.cj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14400.cj1 | 14400y7 | \([0, 0, 0, -31104300, 66769598000]\) | \(1114544804970241/405\) | \(1209323520000000\) | \([2]\) | \(393216\) | \(2.6846\) | |
| 14400.cj2 | 14400y5 | \([0, 0, 0, -1944300, 1042958000]\) | \(272223782641/164025\) | \(489776025600000000\) | \([2, 2]\) | \(196608\) | \(2.3380\) | |
| 14400.cj3 | 14400y8 | \([0, 0, 0, -1584300, 1441118000]\) | \(-147281603041/215233605\) | \(-642684100792320000000\) | \([2]\) | \(393216\) | \(2.6846\) | |
| 14400.cj4 | 14400y3 | \([0, 0, 0, -1152300, -476098000]\) | \(56667352321/15\) | \(44789760000000\) | \([2]\) | \(98304\) | \(1.9915\) | |
| 14400.cj5 | 14400y4 | \([0, 0, 0, -144300, 9758000]\) | \(111284641/50625\) | \(151165440000000000\) | \([2, 2]\) | \(98304\) | \(1.9915\) | |
| 14400.cj6 | 14400y2 | \([0, 0, 0, -72300, -7378000]\) | \(13997521/225\) | \(671846400000000\) | \([2, 2]\) | \(49152\) | \(1.6449\) | |
| 14400.cj7 | 14400y1 | \([0, 0, 0, -300, -322000]\) | \(-1/15\) | \(-44789760000000\) | \([2]\) | \(24576\) | \(1.2983\) | \(\Gamma_0(N)\)-optimal |
| 14400.cj8 | 14400y6 | \([0, 0, 0, 503700, 73262000]\) | \(4733169839/3515625\) | \(-10497600000000000000\) | \([2]\) | \(196608\) | \(2.3380\) |
Rank
sage: E.rank()
The elliptic curves in class 14400.cj have rank \(0\).
Complex multiplication
The elliptic curves in class 14400.cj do not have complex multiplication.Modular form 14400.2.a.cj
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
