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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 8190.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8190.k1 | 8190q3 | \([1, -1, 0, -929854989, -10913430473627]\) | \(121966864931689155376172184529/135006954468750000000\) | \(98420069807718750000000\) | \([2]\) | \(2580480\) | \(3.6983\) | |
| 8190.k2 | 8190q4 | \([1, -1, 0, -142820109, 423732779365]\) | \(441940971557374648005559249/149371122509129665872000\) | \(108891548309155526420688000\) | \([2]\) | \(2580480\) | \(3.6983\) | |
| 8190.k3 | 8190q2 | \([1, -1, 0, -58580109, -167648868635]\) | \(30496269316997451137719249/989901742991616000000\) | \(721638370640888064000000\) | \([2, 2]\) | \(1290240\) | \(3.3517\) | |
| 8190.k4 | 8190q1 | \([1, -1, 0, 1139571, -8997566747]\) | \(224501959288069776431/48100930939256832000\) | \(-35065578654718230528000\) | \([2]\) | \(645120\) | \(3.0052\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8190.k have rank \(1\).
Complex multiplication
The elliptic curves in class 8190.k do not have complex multiplication.Modular form 8190.2.a.k
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.
