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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 6762.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6762.r1 | 6762n2 | \([1, 0, 1, -163980, -22341014]\) | \(4144806984356137/568114785504\) | \(66838136399760096\) | \([2]\) | \(92160\) | \(1.9553\) | |
| 6762.r2 | 6762n1 | \([1, 0, 1, 16340, -1856662]\) | \(4101378352343/15049939968\) | \(-1770610387295232\) | \([2]\) | \(46080\) | \(1.6087\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6762.r have rank \(1\).
Complex multiplication
The elliptic curves in class 6762.r do not have complex multiplication.Modular form 6762.2.a.r
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.
