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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 6006.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6006.l1 | 6006m3 | \([1, 0, 1, -6090767, 5785190210]\) | \(24988464356366680777409257/19820013127858944\) | \(19820013127858944\) | \([4]\) | \(245760\) | \(2.4332\) | |
| 6006.l2 | 6006m2 | \([1, 0, 1, -383247, 89085250]\) | \(6225272619854317474537/171699142176866304\) | \(171699142176866304\) | \([2, 2]\) | \(122880\) | \(2.0867\) | |
| 6006.l3 | 6006m1 | \([1, 0, 1, -55567, -3058366]\) | \(18974193623767438057/6951907079749632\) | \(6951907079749632\) | \([2]\) | \(61440\) | \(1.7401\) | \(\Gamma_0(N)\)-optimal |
| 6006.l4 | 6006m4 | \([1, 0, 1, 81393, 291482434]\) | \(59633809076653006103/36736390236271934208\) | \(-36736390236271934208\) | \([2]\) | \(245760\) | \(2.4332\) |
Rank
sage: E.rank()
The elliptic curves in class 6006.l have rank \(0\).
Complex multiplication
The elliptic curves in class 6006.l do not have complex multiplication.Modular form 6006.2.a.l
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
