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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 450800.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450800.g1 | 450800g2 | \([0, 1, 0, -22143688408, 583576734055188]\) | \(464955364840944779047/212103737413882880\) | \(547785655221185669347082240000000\) | \([2]\) | \(1754726400\) | \(4.9769\) | |
450800.g2 | 450800g1 | \([0, 1, 0, -18631368408, 978326378855188]\) | \(276946345316184817447/168724869939200\) | \(435754053929765804441600000000\) | \([2]\) | \(877363200\) | \(4.6304\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 450800.g have rank \(1\).
Complex multiplication
The elliptic curves in class 450800.g do not have complex multiplication.Modular form 450800.2.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.