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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 30400m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30400.bq1 | 30400m1 | \([0, -1, 0, -92133, 10069637]\) | \(5405726654464/407253125\) | \(6516050000000000\) | \([2]\) | \(184320\) | \(1.7797\) | \(\Gamma_0(N)\)-optimal |
| 30400.bq2 | 30400m2 | \([0, -1, 0, 88367, 44545137]\) | \(298091207216/3525390625\) | \(-902500000000000000\) | \([2]\) | \(368640\) | \(2.1262\) |
Rank
sage: E.rank()
The elliptic curves in class 30400m have rank \(0\).
Complex multiplication
The elliptic curves in class 30400m do not have complex multiplication.Modular form 30400.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
