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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 1400.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1400.g1 | 1400a4 | \([0, 0, 0, -7475, 248750]\) | \(1443468546/7\) | \(224000000\) | \([2]\) | \(1024\) | \(0.80269\) | |
1400.g2 | 1400a3 | \([0, 0, 0, -1475, -17250]\) | \(11090466/2401\) | \(76832000000\) | \([2]\) | \(1024\) | \(0.80269\) | |
1400.g3 | 1400a2 | \([0, 0, 0, -475, 3750]\) | \(740772/49\) | \(784000000\) | \([2, 2]\) | \(512\) | \(0.45611\) | |
1400.g4 | 1400a1 | \([0, 0, 0, 25, 250]\) | \(432/7\) | \(-28000000\) | \([2]\) | \(256\) | \(0.10954\) | \(\Gamma_0(N)\)-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.