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SageMath
E = EllipticCurve("gb1")
E.isogeny_class()
Elliptic curves in class 430950gb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
430950.gb2 | 430950gb1 | \([1, 1, 1, 1605412, -21868177219]\) | \(2761677827/1248480000\) | \(-206867271518797500000000\) | \([2]\) | \(63258624\) | \(3.1530\) | \(\Gamma_0(N)\)-optimal* |
430950.gb1 | 430950gb2 | \([1, 1, 1, -108244588, -422600977219]\) | \(846509996114173/24354723600\) | \(4035463299152942231250000\) | \([2]\) | \(126517248\) | \(3.4995\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 430950gb have rank \(0\).
Complex multiplication
The elliptic curves in class 430950gb do not have complex multiplication.Modular form 430950.2.a.gb
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.