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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 8800c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8800.v2 | 8800c1 | \([0, -1, 0, -104258, 12992012]\) | \(125330290485184/378125\) | \(378125000000\) | \([2]\) | \(23040\) | \(1.4493\) | \(\Gamma_0(N)\)-optimal |
8800.v1 | 8800c2 | \([0, -1, 0, -105633, 12633137]\) | \(2036792051776/107421875\) | \(6875000000000000\) | \([2]\) | \(46080\) | \(1.7958\) |
Rank
sage: E.rank()
The elliptic curves in class 8800c have rank \(1\).
Complex multiplication
The elliptic curves in class 8800c do not have complex multiplication.Modular form 8800.2.a.c
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.