Properties

Label 34914.v
Number of curves $2$
Conductor $34914$
CM no
Rank $0$
Graph

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

Elliptic curves in class 34914.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
34914.v1 34914u2 \([1, 1, 1, -104753, 6506015]\) \(858729462625/371764272\) \(55034454503957808\) \([2]\) \(405504\) \(1.9084\)  
34914.v2 34914u1 \([1, 1, 1, 22207, 767423]\) \(8181353375/6412032\) \(-949210857416448\) \([2]\) \(202752\) \(1.5619\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 34914.v have rank \(0\).

Complex multiplication

The elliptic curves in class 34914.v do not have complex multiplication.

Modular form 34914.2.a.v

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