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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 9702.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9702.z1 | 9702l2 | \([1, -1, 0, -145508253, 675620692613]\) | \(-61279455929796531/681472\) | \(-3788957283325530624\) | \([]\) | \(1088640\) | \(3.1339\) | |
9702.z2 | 9702l1 | \([1, -1, 0, -1700358, 1030640092]\) | \(-71285434106859/18863581528\) | \(-143869362007147212744\) | \([]\) | \(362880\) | \(2.5846\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9702.z have rank \(1\).
Complex multiplication
The elliptic curves in class 9702.z do not have complex multiplication.Modular form 9702.2.a.z
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.