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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 380926g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
380926.g2 | 380926g1 | \([1, 0, 1, -3859119, 3446999714]\) | \(-11192824869409/2563305472\) | \(-1455622361137242468352\) | \([2]\) | \(40255488\) | \(2.7806\) | \(\Gamma_0(N)\)-optimal |
380926.g1 | 380926g2 | \([1, 0, 1, -64807279, 200797141794]\) | \(53008645999484449/2060047808\) | \(1169837807897661576128\) | \([2]\) | \(80510976\) | \(3.1271\) |
Rank
sage: E.rank()
The elliptic curves in class 380926g have rank \(1\).
Complex multiplication
The elliptic curves in class 380926g do not have complex multiplication.Modular form 380926.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.