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SageMath
E = EllipticCurve("lk1")
E.isogeny_class()
Elliptic curves in class 277200.lk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277200.lk1 | 277200lk4 | \([0, 0, 0, -23957200875, 1427216919156250]\) | \(260744057755293612689909/8504954620259328\) | \(49600895345352400896000000000\) | \([2]\) | \(368640000\) | \(4.6002\) | |
| 277200.lk2 | 277200lk3 | \([0, 0, 0, -1562320875, 20258583156250]\) | \(72313087342699809269/11447096545640448\) | \(66759467054175092736000000000\) | \([2]\) | \(184320000\) | \(4.2536\) | |
| 277200.lk3 | 277200lk2 | \([0, 0, 0, -423910875, -3328601093750]\) | \(1444540994277943589/15251205665388\) | \(88945031440542816000000000\) | \([2]\) | \(73728000\) | \(3.7955\) | |
| 277200.lk4 | 277200lk1 | \([0, 0, 0, -422830875, -3346556093750]\) | \(1433528304665250149/162339408\) | \(946763427456000000000\) | \([2]\) | \(36864000\) | \(3.4489\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 277200.lk have rank \(0\).
Complex multiplication
The elliptic curves in class 277200.lk do not have complex multiplication.Modular form 277200.2.a.lk
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.
