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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 129514.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129514.g1 | 129514i2 | \([1, 0, 0, -197232, -33730700]\) | \(1426487591593/2156\) | \(1282439080076\) | \([2]\) | \(802816\) | \(1.5913\) | |
129514.g2 | 129514i1 | \([1, 0, 0, -12212, -538112]\) | \(-338608873/13552\) | \(-8061045646192\) | \([2]\) | \(401408\) | \(1.2448\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 129514.g have rank \(0\).
Complex multiplication
The elliptic curves in class 129514.g do not have complex multiplication.Modular form 129514.2.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.