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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 14490.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14490.g1 | 14490i2 | \([1, -1, 0, -2070, -35154]\) | \(1345938541921/24850350\) | \(18115905150\) | \([2]\) | \(12288\) | \(0.76286\) | |
14490.g2 | 14490i1 | \([1, -1, 0, 0, -1620]\) | \(-1/1555260\) | \(-1133784540\) | \([2]\) | \(6144\) | \(0.41629\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14490.g have rank \(1\).
Complex multiplication
The elliptic curves in class 14490.g do not have complex multiplication.Modular form 14490.2.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.