Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 5850l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5850.ba2 | 5850l1 | \([1, -1, 0, -7317, -237659]\) | \(3803721481/26000\) | \(296156250000\) | \([2]\) | \(13824\) | \(1.0352\) | \(\Gamma_0(N)\)-optimal |
| 5850.ba3 | 5850l2 | \([1, -1, 0, -2817, -530159]\) | \(-217081801/10562500\) | \(-120313476562500\) | \([2]\) | \(27648\) | \(1.3817\) | |
| 5850.ba1 | 5850l3 | \([1, -1, 0, -46692, 3739216]\) | \(988345570681/44994560\) | \(512516160000000\) | \([2]\) | \(41472\) | \(1.5845\) | |
| 5850.ba4 | 5850l4 | \([1, -1, 0, 25308, 14179216]\) | \(157376536199/7722894400\) | \(-87968594025000000\) | \([2]\) | \(82944\) | \(1.9310\) |
Rank
sage: E.rank()
The elliptic curves in class 5850l have rank \(0\).
Complex multiplication
The elliptic curves in class 5850l do not have complex multiplication.Modular form 5850.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
