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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 1950.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1950.g1 | 1950l2 | \([1, 0, 1, -227451, -38491202]\) | \(666276475992821/58199166792\) | \(113670247640625000\) | \([2]\) | \(30720\) | \(2.0132\) | |
1950.g2 | 1950l1 | \([1, 0, 1, -222451, -40401202]\) | \(623295446073461/5458752\) | \(10661625000000\) | \([2]\) | \(15360\) | \(1.6667\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1950.g have rank \(1\).
Complex multiplication
The elliptic curves in class 1950.g do not have complex multiplication.Modular form 1950.2.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 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.