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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 9338.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9338.g1 | 9338f2 | \([1, 0, 0, -368, -92]\) | \(5512402554625/3188422748\) | \(3188422748\) | \([2]\) | \(5376\) | \(0.51304\) | |
9338.g2 | 9338f1 | \([1, 0, 0, 92, 0]\) | \(86058173375/49827568\) | \(-49827568\) | \([2]\) | \(2688\) | \(0.16647\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9338.g have rank \(1\).
Complex multiplication
The elliptic curves in class 9338.g do not have complex multiplication.Modular form 9338.2.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.