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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 5808.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5808.l1 | 5808p3 | \([0, -1, 0, -155888, -23547456]\) | \(57736239625/255552\) | \(1854365518528512\) | \([2]\) | \(34560\) | \(1.7820\) | |
5808.l2 | 5808p4 | \([0, -1, 0, -78448, -47027264]\) | \(-7357983625/127552392\) | \(-925560189435543552\) | \([2]\) | \(69120\) | \(2.1286\) | |
5808.l3 | 5808p1 | \([0, -1, 0, -10688, 404736]\) | \(18609625/1188\) | \(8620500860928\) | \([2]\) | \(11520\) | \(1.2327\) | \(\Gamma_0(N)\)-optimal |
5808.l4 | 5808p2 | \([0, -1, 0, 8672, 1690240]\) | \(9938375/176418\) | \(-1280144377847808\) | \([2]\) | \(23040\) | \(1.5793\) |
Rank
sage: E.rank()
The elliptic curves in class 5808.l have rank \(1\).
Complex multiplication
The elliptic curves in class 5808.l do not have complex multiplication.Modular form 5808.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.