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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 54978.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54978.g1 | 54978g1 | \([1, 1, 0, -75920870, -699250397292]\) | \(-171327409922416869625/648555833326148352\) | \(-183200970509206253942139648\) | \([]\) | \(18724608\) | \(3.7250\) | \(\Gamma_0(N)\)-optimal |
54978.g2 | 54978g2 | \([1, 1, 0, 667968955, 16626151916109]\) | \(116684225008772045300375/490264573250642116608\) | \(-138487607404853871298731835392\) | \([]\) | \(56173824\) | \(4.2743\) |
Rank
sage: E.rank()
The elliptic curves in class 54978.g have rank \(0\).
Complex multiplication
The elliptic curves in class 54978.g do not have complex multiplication.Modular form 54978.2.a.g
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.