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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 2394.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2394.g1 | 2394o2 | \([1, -1, 1, -5387, 153515]\) | \(23711636464489/363888\) | \(265274352\) | \([2]\) | \(4096\) | \(0.75181\) | |
2394.g2 | 2394o1 | \([1, -1, 1, -347, 2315]\) | \(6321363049/715008\) | \(521240832\) | \([2]\) | \(2048\) | \(0.40523\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2394.g have rank \(1\).
Complex multiplication
The elliptic curves in class 2394.g do not have complex multiplication.Modular form 2394.2.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.