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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 2475.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2475.a1 | 2475h3 | \([0, 0, 1, -1759575, 898379406]\) | \(-52893159101157376/11\) | \(-125296875\) | \([]\) | \(21000\) | \(1.8507\) | |
| 2475.a2 | 2475h2 | \([0, 0, 1, -2325, 78156]\) | \(-122023936/161051\) | \(-1834471546875\) | \([]\) | \(4200\) | \(1.0460\) | |
| 2475.a3 | 2475h1 | \([0, 0, 1, -75, -594]\) | \(-4096/11\) | \(-125296875\) | \([]\) | \(840\) | \(0.24130\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2475.a have rank \(0\).
Complex multiplication
The elliptic curves in class 2475.a do not have complex multiplication.Modular form 2475.2.a.a
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.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
