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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 4830c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4830.c1 | 4830c1 | \([1, 1, 0, -3774913, -2823198923]\) | \(5949010462538271898545049/3314625947988102720\) | \(3314625947988102720\) | \([2]\) | \(212160\) | \(2.5012\) | \(\Gamma_0(N)\)-optimal |
4830.c2 | 4830c2 | \([1, 1, 0, -3102633, -3859720227]\) | \(-3303050039017428591035929/4519896503737558217400\) | \(-4519896503737558217400\) | \([2]\) | \(424320\) | \(2.8478\) |
Rank
sage: E.rank()
The elliptic curves in class 4830c have rank \(0\).
Complex multiplication
The elliptic curves in class 4830c do not have complex multiplication.Modular form 4830.2.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.