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SageMath
E = EllipticCurve("gj1")
E.isogeny_class()
Elliptic curves in class 77616.gj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
77616.gj1 | 77616dz1 | \([0, 0, 0, -3381, 78547]\) | \(-84098304/3773\) | \(-191760340464\) | \([]\) | \(110592\) | \(0.92946\) | \(\Gamma_0(N)\)-optimal |
77616.gj2 | 77616dz2 | \([0, 0, 0, 17199, 213003]\) | \(15185664/9317\) | \(-345203834122224\) | \([]\) | \(331776\) | \(1.4788\) |
Rank
sage: E.rank()
The elliptic curves in class 77616.gj have rank \(0\).
Complex multiplication
The elliptic curves in class 77616.gj do not have complex multiplication.Modular form 77616.2.a.gj
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.