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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 3885.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3885.g1 | 3885c4 | \([1, 1, 0, -2828, 56703]\) | \(2502660030961609/983934525\) | \(983934525\) | \([2]\) | \(2560\) | \(0.69014\) | |
3885.g2 | 3885c3 | \([1, 1, 0, -1498, -22523]\) | \(372144896498089/8194921875\) | \(8194921875\) | \([2]\) | \(2560\) | \(0.69014\) | |
3885.g3 | 3885c2 | \([1, 1, 0, -203, 528]\) | \(932288503609/377330625\) | \(377330625\) | \([2, 2]\) | \(1280\) | \(0.34356\) | |
3885.g4 | 3885c1 | \([1, 1, 0, 42, 87]\) | \(7892485271/6662775\) | \(-6662775\) | \([2]\) | \(640\) | \(-0.0030115\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3885.g have rank \(1\).
Complex multiplication
The elliptic curves in class 3885.g do not have complex multiplication.Modular form 3885.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.