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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 79560n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
79560.a1 | 79560n1 | \([0, 0, 0, -56343, -5147638]\) | \(105992740376656/18785\) | \(3505731840\) | \([2]\) | \(172032\) | \(1.2279\) | \(\Gamma_0(N)\)-optimal |
79560.a2 | 79560n2 | \([0, 0, 0, -56163, -5182162]\) | \(-26245032877444/352876225\) | \(-263420690457600\) | \([2]\) | \(344064\) | \(1.5745\) |
Rank
sage: E.rank()
The elliptic curves in class 79560n have rank \(1\).
Complex multiplication
The elliptic curves in class 79560n do not have complex multiplication.Modular form 79560.2.a.n
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.