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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 47432g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47432.n4 | 47432g1 | \([0, 0, 0, 5929, 913066]\) | \(432/7\) | \(-373492905119488\) | \([2]\) | \(122880\) | \(1.4767\) | \(\Gamma_0(N)\)-optimal |
| 47432.n3 | 47432g2 | \([0, 0, 0, -112651, 13695990]\) | \(740772/49\) | \(10457801343345664\) | \([2, 2]\) | \(245760\) | \(1.8233\) | |
| 47432.n2 | 47432g3 | \([0, 0, 0, -349811, -63001554]\) | \(11090466/2401\) | \(1024864531647875072\) | \([2]\) | \(491520\) | \(2.1699\) | |
| 47432.n1 | 47432g4 | \([0, 0, 0, -1772771, 908500670]\) | \(1443468546/7\) | \(2987943240955904\) | \([2]\) | \(491520\) | \(2.1699\) |
Rank
sage: E.rank()
The elliptic curves in class 47432g have rank \(1\).
Complex multiplication
The elliptic curves in class 47432g do not have complex multiplication.Modular form 47432.2.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 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.
