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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 4680g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4680.k4 | 4680g1 | \([0, 0, 0, -183, -3382]\) | \(-3631696/24375\) | \(-4548960000\) | \([2]\) | \(3072\) | \(0.53654\) | \(\Gamma_0(N)\)-optimal |
| 4680.k3 | 4680g2 | \([0, 0, 0, -4683, -123082]\) | \(15214885924/38025\) | \(28385510400\) | \([2, 2]\) | \(6144\) | \(0.88311\) | |
| 4680.k1 | 4680g3 | \([0, 0, 0, -74883, -7887202]\) | \(31103978031362/195\) | \(291133440\) | \([2]\) | \(12288\) | \(1.2297\) | |
| 4680.k2 | 4680g4 | \([0, 0, 0, -6483, -19762]\) | \(20183398562/11567205\) | \(17269744527360\) | \([2]\) | \(12288\) | \(1.2297\) |
Rank
sage: E.rank()
The elliptic curves in class 4680g have rank \(1\).
Complex multiplication
The elliptic curves in class 4680g do not have complex multiplication.Modular form 4680.2.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.
