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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 1848.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1848.l1 | 1848k3 | \([0, 1, 0, -38032, -2867488]\) | \(2970658109581346/2139291\) | \(4381267968\) | \([2]\) | \(4096\) | \(1.1619\) | |
1848.l2 | 1848k4 | \([0, 1, 0, -5472, 90720]\) | \(8849350367426/3314597517\) | \(6788295714816\) | \([2]\) | \(4096\) | \(1.1619\) | |
1848.l3 | 1848k2 | \([0, 1, 0, -2392, -44800]\) | \(1478729816932/38900169\) | \(39833773056\) | \([2, 2]\) | \(2048\) | \(0.81535\) | |
1848.l4 | 1848k1 | \([0, 1, 0, 28, -2208]\) | \(9148592/8301447\) | \(-2125170432\) | \([4]\) | \(1024\) | \(0.46877\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1848.l have rank \(0\).
Complex multiplication
The elliptic curves in class 1848.l do not have complex multiplication.Modular form 1848.2.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.