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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 436800.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
436800.t1 | 436800t3 | \([0, -1, 0, -4569633, 3751027137]\) | \(2576367579235969/8191539720\) | \(33552546693120000000\) | \([2]\) | \(14155776\) | \(2.6133\) | \(\Gamma_0(N)\)-optimal* |
436800.t2 | 436800t4 | \([0, -1, 0, -4441633, -3589644863]\) | \(2365875436837249/8996715000\) | \(36850544640000000000\) | \([2]\) | \(14155776\) | \(2.6133\) | |
436800.t3 | 436800t2 | \([0, -1, 0, -409633, 2867137]\) | \(1855878893569/1073217600\) | \(4395899289600000000\) | \([2, 2]\) | \(7077888\) | \(2.2668\) | \(\Gamma_0(N)\)-optimal* |
436800.t4 | 436800t1 | \([0, -1, 0, 102367, 307137]\) | \(28962726911/16773120\) | \(-68702699520000000\) | \([2]\) | \(3538944\) | \(1.9202\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 436800.t have rank \(0\).
Complex multiplication
The elliptic curves in class 436800.t do not have complex multiplication.Modular form 436800.2.a.t
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.