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SageMath
E = EllipticCurve("en1")
E.isogeny_class()
Elliptic curves in class 76230.en
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76230.en1 | 76230de1 | \([1, -1, 1, -620027, -187354901]\) | \(551105805571803/1376829440\) | \(65856708168007680\) | \([2]\) | \(1433600\) | \(2.1046\) | \(\Gamma_0(N)\)-optimal |
76230.en2 | 76230de2 | \([1, -1, 1, -387707, -329627669]\) | \(-134745327251163/903920796800\) | \(-43236472428894729600\) | \([2]\) | \(2867200\) | \(2.4511\) |
Rank
sage: E.rank()
The elliptic curves in class 76230.en have rank \(1\).
Complex multiplication
The elliptic curves in class 76230.en do not have complex multiplication.Modular form 76230.2.a.en
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.