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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 4830g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4830.f2 | 4830g1 | \([1, 1, 0, -507, -4599]\) | \(14457238157881/49990500\) | \(49990500\) | \([2]\) | \(2304\) | \(0.34029\) | \(\Gamma_0(N)\)-optimal |
4830.f1 | 4830g2 | \([1, 1, 0, -737, -321]\) | \(44365623586201/25674468750\) | \(25674468750\) | \([2]\) | \(4608\) | \(0.68686\) |
Rank
sage: E.rank()
The elliptic curves in class 4830g have rank \(1\).
Complex multiplication
The elliptic curves in class 4830g do not have complex multiplication.Modular form 4830.2.a.g
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.