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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 4830.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4830.v1 | 4830v2 | \([1, 1, 1, -3980, 94925]\) | \(6972359126281921/5071500000\) | \(5071500000\) | \([2]\) | \(7680\) | \(0.79681\) | |
4830.v2 | 4830v1 | \([1, 1, 1, -300, 717]\) | \(2986606123201/1421952000\) | \(1421952000\) | \([2]\) | \(3840\) | \(0.45024\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4830.v have rank \(1\).
Complex multiplication
The elliptic curves in class 4830.v do not have complex multiplication.Modular form 4830.2.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.