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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 9702.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9702.c1 | 9702d2 | \([1, -1, 0, -2969556, -1968891184]\) | \(-61279455929796531/681472\) | \(-32205605515776\) | \([]\) | \(155520\) | \(2.1610\) | |
9702.c2 | 9702d1 | \([1, -1, 0, -34701, -2994867]\) | \(-71285434106859/18863581528\) | \(-1222869399715656\) | \([3]\) | \(51840\) | \(1.6117\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9702.c have rank \(0\).
Complex multiplication
The elliptic curves in class 9702.c do not have complex multiplication.Modular form 9702.2.a.c
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.