Properties

Label 1848.l
Number of curves $4$
Conductor $1848$
CM no
Rank $0$
Graph

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Show commands: 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)
 
\(q + q^{3} + 2 q^{5} - q^{7} + q^{9} + q^{11} + 6 q^{13} + 2 q^{15} + 6 q^{17} + O(q^{20})\) Copy content Toggle raw display

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.