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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 493680c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
493680.c2 | 493680c1 | \([0, -1, 0, -54336, 4892736]\) | \(3254293315259/368475\) | \(2008843161600\) | \([2]\) | \(2027520\) | \(1.3885\) | \(\Gamma_0(N)\)-optimal |
493680.c1 | 493680c2 | \([0, -1, 0, -58736, 4058496]\) | \(4110609334859/1086190605\) | \(5921667871764480\) | \([2]\) | \(4055040\) | \(1.7351\) |
Rank
sage: E.rank()
The elliptic curves in class 493680c have rank \(1\).
Complex multiplication
The elliptic curves in class 493680c do not have complex multiplication.Modular form 493680.2.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.