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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 2475.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2475.g1 | 2475g3 | \([1, -1, 0, -32967, -2293434]\) | \(347873904937/395307\) | \(4502793796875\) | \([2]\) | \(6144\) | \(1.3414\) | |
2475.g2 | 2475g2 | \([1, -1, 0, -2592, -15309]\) | \(169112377/88209\) | \(1004755640625\) | \([2, 2]\) | \(3072\) | \(0.99482\) | |
2475.g3 | 2475g1 | \([1, -1, 0, -1467, 21816]\) | \(30664297/297\) | \(3383015625\) | \([2]\) | \(1536\) | \(0.64825\) | \(\Gamma_0(N)\)-optimal |
2475.g4 | 2475g4 | \([1, -1, 0, 9783, -126684]\) | \(9090072503/5845851\) | \(-66587896546875\) | \([2]\) | \(6144\) | \(1.3414\) |
Rank
sage: E.rank()
The elliptic curves in class 2475.g have rank \(0\).
Complex multiplication
The elliptic curves in class 2475.g do not have complex multiplication.Modular form 2475.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.