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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 2300.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2300.g1 | 2300f2 | \([0, -1, 0, -27708, -1746088]\) | \(941054800/12167\) | \(30417500000000\) | \([]\) | \(7560\) | \(1.3954\) | |
2300.g2 | 2300f1 | \([0, -1, 0, -2708, 53912]\) | \(878800/23\) | \(57500000000\) | \([]\) | \(2520\) | \(0.84612\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2300.g have rank \(1\).
Complex multiplication
The elliptic curves in class 2300.g do not have complex multiplication.Modular form 2300.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.