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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 88935.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
88935.p1 | 88935bd1 | \([1, 1, 1, -80165, -5340070]\) | \(205379/75\) | \(20805764092384425\) | \([2]\) | \(760320\) | \(1.8315\) | \(\Gamma_0(N)\)-optimal |
88935.p2 | 88935bd2 | \([1, 1, 1, 245930, -37427818]\) | \(5929741/5625\) | \(-1560432306928831875\) | \([2]\) | \(1520640\) | \(2.1781\) |
Rank
sage: E.rank()
The elliptic curves in class 88935.p have rank \(1\).
Complex multiplication
The elliptic curves in class 88935.p do not have complex multiplication.Modular form 88935.2.a.p
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.