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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 3179.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3179.a1 | 3179c3 | \([0, 1, 1, -2260076, -1308527588]\) | \(-52893159101157376/11\) | \(-265513259\) | \([]\) | \(25600\) | \(1.9133\) | |
3179.a2 | 3179c2 | \([0, 1, 1, -2986, -114768]\) | \(-122023936/161051\) | \(-3887379625019\) | \([]\) | \(5120\) | \(1.1086\) | |
3179.a3 | 3179c1 | \([0, 1, 1, -96, 832]\) | \(-4096/11\) | \(-265513259\) | \([]\) | \(1024\) | \(0.30388\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3179.a have rank \(1\).
Complex multiplication
The elliptic curves in class 3179.a do not have complex multiplication.Modular form 3179.2.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.