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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 116688.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116688.l1 | 116688s4 | \([0, -1, 0, -672672, 212501952]\) | \(8218157522273610913/3262914972603\) | \(13364899727781888\) | \([4]\) | \(983040\) | \(2.0583\) | |
| 116688.l2 | 116688s3 | \([0, -1, 0, -357312, -80521920]\) | \(1231708064988053953/26933399479701\) | \(110319204268855296\) | \([2]\) | \(983040\) | \(2.0583\) | |
| 116688.l3 | 116688s2 | \([0, -1, 0, -48432, 2257920]\) | \(3067396672113073/1245074357241\) | \(5099824567259136\) | \([2, 2]\) | \(491520\) | \(1.7118\) | |
| 116688.l4 | 116688s1 | \([0, -1, 0, 9888, 251712]\) | \(26100282937247/21962862207\) | \(-89959883599872\) | \([2]\) | \(245760\) | \(1.3652\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116688.l have rank \(0\).
Complex multiplication
The elliptic curves in class 116688.l do not have complex multiplication.Modular form 116688.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
