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SageMath
sage: E = EllipticCurve("g1")
sage: E.isogeny_class()
Elliptic curves in class 1400.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
1400.g1 | 1400a4 | [0, 0, 0, -7475, 248750] | [2] | 1024 | |
1400.g2 | 1400a3 | [0, 0, 0, -1475, -17250] | [2] | 1024 | |
1400.g3 | 1400a2 | [0, 0, 0, -475, 3750] | [2, 2] | 512 | |
1400.g4 | 1400a1 | [0, 0, 0, 25, 250] | [2] | 256 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1400.g have rank \(0\).
Complex multiplication
The elliptic curves in class 1400.g do not have complex multiplication.Modular form 1400.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.