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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 10304s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10304.bg2 | 10304s1 | \([0, -1, 0, -257, -1375]\) | \(7189057/644\) | \(168820736\) | \([2]\) | \(4608\) | \(0.31846\) | \(\Gamma_0(N)\)-optimal |
10304.bg1 | 10304s2 | \([0, -1, 0, -897, 8993]\) | \(304821217/51842\) | \(13590069248\) | \([2]\) | \(9216\) | \(0.66503\) |
Rank
sage: E.rank()
The elliptic curves in class 10304s have rank \(0\).
Complex multiplication
The elliptic curves in class 10304s do not have complex multiplication.Modular form 10304.2.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.