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SageMath
E = EllipticCurve("ea1")
E.isogeny_class()
Elliptic curves in class 394944ea
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 394944.ea2 | 394944ea1 | \([0, -1, 0, -4232257, -3277691327]\) | \(18052771191337/444958272\) | \(206640439965146677248\) | \([2]\) | \(15482880\) | \(2.6819\) | \(\Gamma_0(N)\)-optimal |
| 394944.ea1 | 394944ea2 | \([0, -1, 0, -9498177, 6509547585]\) | \(204055591784617/78708537864\) | \(36552566648834805989376\) | \([2]\) | \(30965760\) | \(3.0284\) |
Rank
sage: E.rank()
The elliptic curves in class 394944ea have rank \(1\).
Complex multiplication
The elliptic curves in class 394944ea do not have complex multiplication.Modular form 394944.2.a.ea
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.
