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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 363090l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 363090.l4 | 363090l1 | \([1, 1, 0, -873303, -43740843]\) | \(626081837627249641/355406899411200\) | \(41813266308828268800\) | \([2]\) | \(11010048\) | \(2.4549\) | \(\Gamma_0(N)\)-optimal |
| 363090.l2 | 363090l2 | \([1, 1, 0, -10285223, -12676419867]\) | \(1022766924906322301161/2228000482890000\) | \(262122028811525610000\) | \([2, 2]\) | \(22020096\) | \(2.8015\) | |
| 363090.l3 | 363090l3 | \([1, 1, 0, -6683723, -21678008967]\) | \(-280666708617128357161/1562710596384182700\) | \(-183851338954002710472300\) | \([2]\) | \(44040192\) | \(3.1480\) | |
| 363090.l1 | 363090l4 | \([1, 1, 0, -164477443, -811978049903]\) | \(4182678783098919567271081/19913217187500\) | \(2342770088892187500\) | \([2]\) | \(44040192\) | \(3.1480\) |
Rank
sage: E.rank()
The elliptic curves in class 363090l have rank \(1\).
Complex multiplication
The elliptic curves in class 363090l do not have complex multiplication.Modular form 363090.2.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.
