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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 6800.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6800.v1 | 6800l1 | \([0, -1, 0, -3408, 77312]\) | \(68417929/425\) | \(27200000000\) | \([2]\) | \(6144\) | \(0.84018\) | \(\Gamma_0(N)\)-optimal |
| 6800.v2 | 6800l2 | \([0, -1, 0, -1408, 165312]\) | \(-4826809/180625\) | \(-11560000000000\) | \([2]\) | \(12288\) | \(1.1868\) |
Rank
sage: E.rank()
The elliptic curves in class 6800.v have rank \(0\).
Complex multiplication
The elliptic curves in class 6800.v do not have complex multiplication.Modular form 6800.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
