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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 10626q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10626.s2 | 10626q1 | \([1, 0, 0, -3878, 92736]\) | \(-6449916994998625/8532911772\) | \(-8532911772\) | \([2]\) | \(10752\) | \(0.81201\) | \(\Gamma_0(N)\)-optimal |
10626.s1 | 10626q2 | \([1, 0, 0, -62068, 5946650]\) | \(26444015547214434625/46191222\) | \(46191222\) | \([2]\) | \(21504\) | \(1.1586\) |
Rank
sage: E.rank()
The elliptic curves in class 10626q have rank \(0\).
Complex multiplication
The elliptic curves in class 10626q do not have complex multiplication.Modular form 10626.2.a.q
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.