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SageMath
E = EllipticCurve("ll1")
E.isogeny_class()
Elliptic curves in class 369600.ll
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.ll1 | 369600ll4 | \([0, -1, 0, -10647644833, -422875537942463]\) | \(260744057755293612689909/8504954620259328\) | \(4354536765572775936000000000\) | \([2]\) | \(368640000\) | \(4.3974\) | |
| 369600.ll2 | 369600ll3 | \([0, -1, 0, -694364833, -6002311702463]\) | \(72313087342699809269/11447096545640448\) | \(5860913431367909376000000000\) | \([2]\) | \(184320000\) | \(4.0509\) | |
| 369600.ll3 | 369600ll2 | \([0, -1, 0, -188404833, 986314977537]\) | \(1444540994277943589/15251205665388\) | \(7808617300678656000000000\) | \([2]\) | \(73728000\) | \(3.5927\) | |
| 369600.ll4 | 369600ll1 | \([0, -1, 0, -187924833, 991634817537]\) | \(1433528304665250149/162339408\) | \(83117776896000000000\) | \([2]\) | \(36864000\) | \(3.2462\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 369600.ll have rank \(1\).
Complex multiplication
The elliptic curves in class 369600.ll do not have complex multiplication.Modular form 369600.2.a.ll
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
