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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 2925f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2925.p4 | 2925f1 | \([1, -1, 0, 108, 891]\) | \(12167/39\) | \(-444234375\) | \([2]\) | \(1024\) | \(0.34251\) | \(\Gamma_0(N)\)-optimal |
2925.p3 | 2925f2 | \([1, -1, 0, -1017, 11016]\) | \(10218313/1521\) | \(17325140625\) | \([2, 2]\) | \(2048\) | \(0.68909\) | |
2925.p2 | 2925f3 | \([1, -1, 0, -4392, -100359]\) | \(822656953/85683\) | \(975982921875\) | \([2]\) | \(4096\) | \(1.0357\) | |
2925.p1 | 2925f4 | \([1, -1, 0, -15642, 756891]\) | \(37159393753/1053\) | \(11994328125\) | \([2]\) | \(4096\) | \(1.0357\) |
Rank
sage: E.rank()
The elliptic curves in class 2925f have rank \(0\).
Complex multiplication
The elliptic curves in class 2925f do not have complex multiplication.Modular form 2925.2.a.f
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 Cremona 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 Cremona labels.