Properties

Label 1848.e
Number of curves $2$
Conductor $1848$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 1848.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1848.e1 1848e2 \([0, 1, 0, -56600, -5201616]\) \(9791533777258802/427901859\) \(876343007232\) \([2]\) \(7680\) \(1.3698\)  
1848.e2 1848e1 \([0, 1, 0, -3360, -90576]\) \(-4097989445764/1004475087\) \(-1028582489088\) \([2]\) \(3840\) \(1.0232\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1848.e have rank \(0\).

Complex multiplication

The elliptic curves in class 1848.e do not have complex multiplication.

Modular form 1848.2.a.e

sage: E.q_eigenform(10)
 
\(q + q^{3} - 4 q^{5} - q^{7} + q^{9} - q^{11} - 2 q^{13} - 4 q^{15} + 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.