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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 20691m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20691.l2 | 20691m1 | \([0, 0, 1, -395670, -103271292]\) | \(-5304438784000/497763387\) | \(-642845470451451003\) | \([]\) | \(172800\) | \(2.1591\) | \(\Gamma_0(N)\)-optimal |
| 20691.l1 | 20691m2 | \([0, 0, 1, -32738970, -72101721123]\) | \(-3004935183806464000/2037123\) | \(-2630879103413187\) | \([]\) | \(518400\) | \(2.7084\) |
Rank
sage: E.rank()
The elliptic curves in class 20691m have rank \(1\).
Complex multiplication
The elliptic curves in class 20691m do not have complex multiplication.Modular form 20691.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
