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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 27209.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 27209.l1 | 27209d4 | \([1, -1, 0, -20903, 1168194]\) | \(209267191953/55223\) | \(266550873407\) | \([2]\) | \(38400\) | \(1.1768\) | |
| 27209.l2 | 27209d2 | \([1, -1, 0, -1468, 13755]\) | \(72511713/25921\) | \(125115716089\) | \([2, 2]\) | \(19200\) | \(0.83027\) | |
| 27209.l3 | 27209d1 | \([1, -1, 0, -623, -5680]\) | \(5545233/161\) | \(777116249\) | \([2]\) | \(9600\) | \(0.48369\) | \(\Gamma_0(N)\)-optimal |
| 27209.l4 | 27209d3 | \([1, -1, 0, 4447, 93016]\) | \(2014698447/1958887\) | \(-9455173401583\) | \([2]\) | \(38400\) | \(1.1768\) |
Rank
sage: E.rank()
The elliptic curves in class 27209.l have rank \(1\).
Complex multiplication
The elliptic curves in class 27209.l do not have complex multiplication.Modular form 27209.2.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.
