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Properties

Label 232050.ev
Number of curves $2$
Conductor $232050$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ev1")
 
E.isogeny_class()
 

Elliptic curves in class 232050.ev

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
232050.ev1 232050ev1 \([1, 1, 1, -12338, 292031]\) \(13293525831769/5251384320\) \(82052880000000\) \([2]\) \(1105920\) \(1.3683\) \(\Gamma_0(N)\)-optimal
232050.ev2 232050ev2 \([1, 1, 1, 39662, 2164031]\) \(441597730070951/383060714400\) \(-5985323662500000\) \([2]\) \(2211840\) \(1.7149\)  

Rank

sage: E.rank()
 

The elliptic curves in class 232050.ev have rank \(1\).

Complex multiplication

The elliptic curves in class 232050.ev do not have complex multiplication.

Modular form 232050.2.a.ev

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} - q^{7} + q^{8} + q^{9} + 6 q^{11} - q^{12} - q^{13} - q^{14} + q^{16} + q^{17} + q^{18} - 6 q^{19} + O(q^{20})\) 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.