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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 443760s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
443760.s2 | 443760s1 | \([0, -1, 0, -185516, 119846496]\) | \(-5488/45\) | \(-5789866889512431360\) | \([2]\) | \(8233984\) | \(2.2830\) | \(\Gamma_0(N)\)-optimal* |
443760.s1 | 443760s2 | \([0, -1, 0, -4955936, 4237673040]\) | \(26156812/75\) | \(38599112596749542400\) | \([2]\) | \(16467968\) | \(2.6296\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 443760s have rank \(1\).
Complex multiplication
The elliptic curves in class 443760s do not have complex multiplication.Modular form 443760.2.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.