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SageMath
E = EllipticCurve("fx1")
E.isogeny_class()
Elliptic curves in class 77616.fx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
77616.fx1 | 77616du2 | \([0, 0, 0, -3669939, -2706053518]\) | \(144106117295241933/247808\) | \(9400114741248\) | \([2]\) | \(946176\) | \(2.1782\) | |
77616.fx2 | 77616du1 | \([0, 0, 0, -229299, -42310030]\) | \(-35148950502093/46137344\) | \(-1750130453643264\) | \([2]\) | \(473088\) | \(1.8316\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 77616.fx have rank \(0\).
Complex multiplication
The elliptic curves in class 77616.fx do not have complex multiplication.Modular form 77616.2.a.fx
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.