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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 19320g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19320.q1 | 19320g1 | \([0, 1, 0, -96, -336]\) | \(96550276/16905\) | \(17310720\) | \([2]\) | \(4352\) | \(0.10873\) | \(\Gamma_0(N)\)-optimal |
19320.q2 | 19320g2 | \([0, 1, 0, 184, -1680]\) | \(334568302/833175\) | \(-1706342400\) | \([2]\) | \(8704\) | \(0.45530\) |
Rank
sage: E.rank()
The elliptic curves in class 19320g have rank \(0\).
Complex multiplication
The elliptic curves in class 19320g do not have complex multiplication.Modular form 19320.2.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.