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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 5355g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5355.p3 | 5355g1 | \([1, -1, 0, -3015, 64480]\) | \(4158523459441/16065\) | \(11711385\) | \([2]\) | \(3072\) | \(0.56981\) | \(\Gamma_0(N)\)-optimal |
| 5355.p2 | 5355g2 | \([1, -1, 0, -3060, 62491]\) | \(4347507044161/258084225\) | \(188143400025\) | \([2, 2]\) | \(6144\) | \(0.91638\) | |
| 5355.p1 | 5355g3 | \([1, -1, 0, -9135, -257054]\) | \(115650783909361/27072079335\) | \(19735545835215\) | \([2]\) | \(12288\) | \(1.2630\) | |
| 5355.p4 | 5355g4 | \([1, -1, 0, 2295, 254200]\) | \(1833318007919/39525924375\) | \(-28814398869375\) | \([2]\) | \(12288\) | \(1.2630\) |
Rank
sage: E.rank()
The elliptic curves in class 5355g have rank \(1\).
Complex multiplication
The elliptic curves in class 5355g do not have complex multiplication.Modular form 5355.2.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.
