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SageMath
E = EllipticCurve("ge1")
E.isogeny_class()
Elliptic curves in class 97344ge
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97344.d1 | 97344ge1 | \([0, 0, 0, -3962712, 2852496920]\) | \(1909913257984/129730653\) | \(467444660074706875392\) | \([2]\) | \(5160960\) | \(2.7147\) | \(\Gamma_0(N)\)-optimal |
| 97344.d2 | 97344ge2 | \([0, 0, 0, 3429348, 12269981360]\) | \(77366117936/1172914587\) | \(-67619813542988049727488\) | \([2]\) | \(10321920\) | \(3.0613\) |
Rank
sage: E.rank()
The elliptic curves in class 97344ge have rank \(1\).
Complex multiplication
The elliptic curves in class 97344ge do not have complex multiplication.Modular form 97344.2.a.ge
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.
