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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 10350.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10350.m1 | 10350p3 | \([1, -1, 0, -331317, 73485841]\) | \(353108405631241/172500\) | \(1964882812500\) | \([2]\) | \(49152\) | \(1.6939\) | |
| 10350.m2 | 10350p2 | \([1, -1, 0, -20817, 1139341]\) | \(87587538121/1904400\) | \(21692306250000\) | \([2, 2]\) | \(24576\) | \(1.3474\) | |
| 10350.m3 | 10350p1 | \([1, -1, 0, -2817, -30659]\) | \(217081801/88320\) | \(1006020000000\) | \([2]\) | \(12288\) | \(1.0008\) | \(\Gamma_0(N)\)-optimal |
| 10350.m4 | 10350p4 | \([1, -1, 0, 1683, 3456841]\) | \(46268279/453342420\) | \(-5163853502812500\) | \([2]\) | \(49152\) | \(1.6939\) |
Rank
sage: E.rank()
The elliptic curves in class 10350.m have rank \(1\).
Complex multiplication
The elliptic curves in class 10350.m do not have complex multiplication.Modular form 10350.2.a.m
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
