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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 262080.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 262080.l1 | 262080l3 | \([0, 0, 0, -757876908, 8030383101232]\) | \(251913989442882736925929/6620155222590000\) | \(1265131364618891427840000\) | \([2]\) | \(75497472\) | \(3.7306\) | |
| 262080.l2 | 262080l2 | \([0, 0, 0, -49212588, 115169578288]\) | \(68973914606086620649/9931302391046400\) | \(1897901442484882794086400\) | \([2, 2]\) | \(37748736\) | \(3.3840\) | |
| 262080.l3 | 262080l1 | \([0, 0, 0, -13085868, -16432837328]\) | \(1296772724742600169/140009392373760\) | \(26756211550577240309760\) | \([2]\) | \(18874368\) | \(3.0374\) | \(\Gamma_0(N)\)-optimal |
| 262080.l4 | 262080l4 | \([0, 0, 0, 81424212, 622510654768]\) | \(312404265277724598551/1056801141155738160\) | \(-201957843115057641852764160\) | \([2]\) | \(75497472\) | \(3.7306\) |
Rank
sage: E.rank()
The elliptic curves in class 262080.l have rank \(1\).
Complex multiplication
The elliptic curves in class 262080.l do not have complex multiplication.Modular form 262080.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
