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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 2310e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2310.e1 | 2310e1 | \([1, 0, 1, -169, -724]\) | \(529278808969/88704000\) | \(88704000\) | \([2]\) | \(960\) | \(0.24613\) | \(\Gamma_0(N)\)-optimal |
2310.e2 | 2310e2 | \([1, 0, 1, 311, -3988]\) | \(3342032927351/8893500000\) | \(-8893500000\) | \([2]\) | \(1920\) | \(0.59271\) |
Rank
sage: E.rank()
The elliptic curves in class 2310e have rank \(0\).
Complex multiplication
The elliptic curves in class 2310e do not have complex multiplication.Modular form 2310.2.a.e
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.