Properties

Label 155848.v
Number of curves $2$
Conductor $155848$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 155848.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
155848.v1 155848n2 \([0, -1, 0, -59088, -5508292]\) \(12576878500/1127\) \(2044466428928\) \([2]\) \(409600\) \(1.4022\)  
155848.v2 155848n1 \([0, -1, 0, -3428, -98140]\) \(-9826000/3703\) \(-1679383138048\) \([2]\) \(204800\) \(1.0556\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 155848.v have rank \(1\).

Complex multiplication

The elliptic curves in class 155848.v do not have complex multiplication.

Modular form 155848.2.a.v

sage: E.q_eigenform(10)
 
\(q + 2q^{3} + q^{7} + q^{9} - 6q^{13} + O(q^{20})\)  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.