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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 8976.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8976.s1 | 8976q1 | \([0, -1, 0, -3136, 68608]\) | \(832972004929/610368\) | \(2500067328\) | \([2]\) | \(9216\) | \(0.73752\) | \(\Gamma_0(N)\)-optimal |
8976.s2 | 8976q2 | \([0, -1, 0, -2496, 96768]\) | \(-420021471169/727634952\) | \(-2980392763392\) | \([2]\) | \(18432\) | \(1.0841\) |
Rank
sage: E.rank()
The elliptic curves in class 8976.s have rank \(0\).
Complex multiplication
The elliptic curves in class 8976.s do not have complex multiplication.Modular form 8976.2.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.