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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 435120s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435120.s2 | 435120s1 | \([0, -1, 0, 3344, 57856]\) | \(2942649737/2772225\) | \(-3894776524800\) | \([2]\) | \(786432\) | \(1.1031\) | \(\Gamma_0(N)\)-optimal* |
435120.s1 | 435120s2 | \([0, -1, 0, -17376, 538560]\) | \(412994303623/151723125\) | \(213160066560000\) | \([2]\) | \(1572864\) | \(1.4496\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 435120s have rank \(2\).
Complex multiplication
The elliptic curves in class 435120s do not have complex multiplication.Modular form 435120.2.a.s
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.