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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 11760f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11760.c4 | 11760f1 | \([0, -1, 0, -36031, 2644510]\) | \(2748251600896/2205\) | \(4150656720\) | \([2]\) | \(24576\) | \(1.1510\) | \(\Gamma_0(N)\)-optimal |
| 11760.c3 | 11760f2 | \([0, -1, 0, -36276, 2606976]\) | \(175293437776/4862025\) | \(146435169081600\) | \([2, 2]\) | \(49152\) | \(1.4976\) | |
| 11760.c2 | 11760f3 | \([0, -1, 0, -84296, -5690880]\) | \(549871953124/200930625\) | \(24206629991040000\) | \([2, 2]\) | \(98304\) | \(1.8441\) | |
| 11760.c5 | 11760f4 | \([0, -1, 0, 7824, 8498736]\) | \(439608956/259416045\) | \(-31252519196881920\) | \([2]\) | \(98304\) | \(1.8441\) | |
| 11760.c1 | 11760f5 | \([0, -1, 0, -1195616, -502673184]\) | \(784478485879202/221484375\) | \(53365586400000000\) | \([2]\) | \(196608\) | \(2.1907\) | |
| 11760.c6 | 11760f6 | \([0, -1, 0, 258704, -40539680]\) | \(7947184069438/7533176175\) | \(-1815082278528153600\) | \([2]\) | \(196608\) | \(2.1907\) |
Rank
sage: E.rank()
The elliptic curves in class 11760f have rank \(0\).
Complex multiplication
The elliptic curves in class 11760f do not have complex multiplication.Modular form 11760.2.a.f
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 Cremona numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
