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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 2646.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2646.g1 | 2646a1 | \([1, -1, 0, -177, -883]\) | \(-637875/16\) | \(-15431472\) | \([]\) | \(864\) | \(0.16367\) | \(\Gamma_0(N)\)-optimal |
2646.g2 | 2646a2 | \([1, -1, 0, 768, -4096]\) | \(5767125/4096\) | \(-35554111488\) | \([]\) | \(2592\) | \(0.71297\) |
Rank
sage: E.rank()
The elliptic curves in class 2646.g have rank \(0\).
Complex multiplication
The elliptic curves in class 2646.g do not have complex multiplication.Modular form 2646.2.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.