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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 250470.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
250470.s1 | 250470s2 | \([1, -1, 0, -1895790, 1004726300]\) | \(15753412685361987/8001125000\) | \(382710987165375000\) | \([2]\) | \(5529600\) | \(2.3258\) | |
250470.s2 | 250470s1 | \([1, -1, 0, -138870, 9958196]\) | \(6191999358147/2693944000\) | \(128857125417768000\) | \([2]\) | \(2764800\) | \(1.9792\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 250470.s have rank \(0\).
Complex multiplication
The elliptic curves in class 250470.s do not have complex multiplication.Modular form 250470.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.