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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 363726.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
363726.s1 | 363726s2 | \([1, -1, 0, -485172, -2379577392]\) | \(-9779750241625/1888619876352\) | \(-2439092075925348569088\) | \([]\) | \(16588800\) | \(2.7831\) | |
363726.s2 | 363726s1 | \([1, -1, 0, 53883, 87892965]\) | \(13396484375/2592638928\) | \(-3348310130694497232\) | \([]\) | \(5529600\) | \(2.2338\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 363726.s have rank \(1\).
Complex multiplication
The elliptic curves in class 363726.s do not have complex multiplication.Modular form 363726.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.