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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 58950.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58950.m1 | 58950h4 | \([1, -1, 0, -1257642, -542540484]\) | \(19312898130234073/84888\) | \(966927375000\) | \([2]\) | \(589824\) | \(1.9281\) | |
| 58950.m2 | 58950h2 | \([1, -1, 0, -78642, -8453484]\) | \(4722184089433/9884736\) | \(112593321000000\) | \([2, 2]\) | \(294912\) | \(1.5815\) | |
| 58950.m3 | 58950h3 | \([1, -1, 0, -51642, -14366484]\) | \(-1337180541913/7067998104\) | \(-80508915903375000\) | \([2]\) | \(589824\) | \(1.9281\) | |
| 58950.m4 | 58950h1 | \([1, -1, 0, -6642, -29484]\) | \(2845178713/1609728\) | \(18335808000000\) | \([2]\) | \(147456\) | \(1.2350\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 58950.m have rank \(0\).
Complex multiplication
The elliptic curves in class 58950.m do not have complex multiplication.Modular form 58950.2.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.
