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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 35490.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35490.l1 | 35490i6 | \([1, 1, 0, -10336888, -12796140482]\) | \(25306558948218234961/4478906250\) | \(21618824997656250\) | \([2]\) | \(1376256\) | \(2.5309\) | |
| 35490.l2 | 35490i4 | \([1, 1, 0, -648118, -198801728]\) | \(6237734630203441/82168222500\) | \(396610315877002500\) | \([2, 2]\) | \(688128\) | \(2.1843\) | |
| 35490.l3 | 35490i5 | \([1, 1, 0, -98868, -524287278]\) | \(-22143063655441/24584858584650\) | \(-118666416680115881850\) | \([2]\) | \(1376256\) | \(2.5309\) | |
| 35490.l4 | 35490i2 | \([1, 1, 0, -76898, 3295908]\) | \(10418796526321/5038160400\) | \(24318237962163600\) | \([2, 2]\) | \(344064\) | \(1.8378\) | |
| 35490.l5 | 35490i1 | \([1, 1, 0, -63378, 6110772]\) | \(5832972054001/4542720\) | \(21926841780480\) | \([2]\) | \(172032\) | \(1.4912\) | \(\Gamma_0(N)\)-optimal |
| 35490.l6 | 35490i3 | \([1, 1, 0, 278002, 25512648]\) | \(492271755328079/342606902820\) | \(-1653698081993701380\) | \([2]\) | \(688128\) | \(2.1843\) |
Rank
sage: E.rank()
The elliptic curves in class 35490.l have rank \(0\).
Complex multiplication
The elliptic curves in class 35490.l do not have complex multiplication.Modular form 35490.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
