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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 5776.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5776.g1 | 5776i2 | \([0, -1, 0, -537288, 152036848]\) | \(-246579625/512\) | \(-35617113198559232\) | \([]\) | \(49248\) | \(2.0618\) | |
5776.g2 | 5776i1 | \([0, -1, 0, 11432, 1029104]\) | \(2375/8\) | \(-556517393727488\) | \([]\) | \(16416\) | \(1.5125\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5776.g have rank \(0\).
Complex multiplication
The elliptic curves in class 5776.g do not have complex multiplication.Modular form 5776.2.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.