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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 101640.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101640.l1 | 101640f4 | \([0, -1, 0, -3602936, -2630652660]\) | \(1425631925916578/270703125\) | \(982153418400000000\) | \([2]\) | \(1966080\) | \(2.4535\) | |
101640.l2 | 101640f3 | \([0, -1, 0, -1579816, 740631916]\) | \(120186986927618/4332064275\) | \(15717409011882547200\) | \([2]\) | \(1966080\) | \(2.4535\) | |
101640.l3 | 101640f2 | \([0, -1, 0, -248816, -31880484]\) | \(939083699236/300155625\) | \(544505855160960000\) | \([2, 2]\) | \(983040\) | \(2.1069\) | |
101640.l4 | 101640f1 | \([0, -1, 0, 44004, -3418380]\) | \(20777545136/23059575\) | \(-10457969599123200\) | \([2]\) | \(491520\) | \(1.7603\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 101640.l have rank \(1\).
Complex multiplication
The elliptic curves in class 101640.l do not have complex multiplication.Modular form 101640.2.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.