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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 5070.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5070.u1 | 5070w4 | \([1, 0, 0, -14623320, 21522489312]\) | \(71647584155243142409/10140000\) | \(48943843260000\) | \([2]\) | \(215040\) | \(2.4797\) | |
| 5070.u2 | 5070w3 | \([1, 0, 0, -1049240, 230144160]\) | \(26465989780414729/10571870144160\) | \(51028397958662785440\) | \([2]\) | \(215040\) | \(2.4797\) | |
| 5070.u3 | 5070w2 | \([1, 0, 0, -914040, 336168000]\) | \(17496824387403529/6580454400\) | \(31762596522009600\) | \([2, 2]\) | \(107520\) | \(2.1332\) | |
| 5070.u4 | 5070w1 | \([1, 0, 0, -48760, 6842432]\) | \(-2656166199049/2658140160\) | \(-12830334847549440\) | \([2]\) | \(53760\) | \(1.7866\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5070.u have rank \(0\).
Complex multiplication
The elliptic curves in class 5070.u do not have complex multiplication.Modular form 5070.2.a.u
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
