Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 39270l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39270.n4 | 39270l1 | \([1, 1, 0, 10098, 2715444]\) | \(113857753216578839/3241437293445120\) | \(-3241437293445120\) | \([2]\) | \(245760\) | \(1.6563\) | \(\Gamma_0(N)\)-optimal |
| 39270.n3 | 39270l2 | \([1, 1, 0, -240782, 43207476]\) | \(1543826825235935349481/83173913985254400\) | \(83173913985254400\) | \([2, 2]\) | \(491520\) | \(2.0029\) | |
| 39270.n2 | 39270l3 | \([1, 1, 0, -694382, -168079404]\) | \(37027130142709543835881/9265420909010740320\) | \(9265420909010740320\) | \([2]\) | \(983040\) | \(2.3495\) | |
| 39270.n1 | 39270l4 | \([1, 1, 0, -3801262, 2851002004]\) | \(6074454775981549220461801/19158373648260000\) | \(19158373648260000\) | \([2]\) | \(983040\) | \(2.3495\) |
Rank
sage: E.rank()
The elliptic curves in class 39270l have rank \(0\).
Complex multiplication
The elliptic curves in class 39270l do not have complex multiplication.Modular form 39270.2.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 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.
