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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 6762.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6762.c1 | 6762h1 | \([1, 1, 0, -2146, 34420]\) | \(3188856056959/274710528\) | \(94225711104\) | \([2]\) | \(10752\) | \(0.84674\) | \(\Gamma_0(N)\)-optimal |
6762.c2 | 6762h2 | \([1, 1, 0, 2334, 164340]\) | \(4096768048001/35984932992\) | \(-12342832016256\) | \([2]\) | \(21504\) | \(1.1933\) |
Rank
sage: E.rank()
The elliptic curves in class 6762.c have rank \(1\).
Complex multiplication
The elliptic curves in class 6762.c do not have complex multiplication.Modular form 6762.2.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 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.