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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 53550.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53550.g1 | 53550bg1 | \([1, -1, 0, -2070117, -1146020459]\) | \(-137810063865625/17608192\) | \(-125355195000000000\) | \([]\) | \(1244160\) | \(2.3023\) | \(\Gamma_0(N)\)-optimal |
53550.g2 | 53550bg2 | \([1, -1, 0, 320508, -3590673584]\) | \(511460384375/782623571968\) | \(-5571607265280000000000\) | \([]\) | \(3732480\) | \(2.8516\) |
Rank
sage: E.rank()
The elliptic curves in class 53550.g have rank \(1\).
Complex multiplication
The elliptic curves in class 53550.g do not have complex multiplication.Modular form 53550.2.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.