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Properties

Label 19950bv
Number of curves $2$
Conductor $19950$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bv1")
 
E.isogeny_class()
 

Elliptic curves in class 19950bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19950.bq1 19950bv1 \([1, 1, 1, -65303, 6419261]\) \(-1231922871794037145/5186378855952\) \(-129659471398800\) \([]\) \(103680\) \(1.5627\) \(\Gamma_0(N)\)-optimal
19950.bq2 19950bv2 \([1, 1, 1, 152722, 34054571]\) \(15757536948921630455/29083977048526848\) \(-727099426213171200\) \([]\) \(311040\) \(2.1120\)  

Rank

sage: E.rank()
 

The elliptic curves in class 19950bv have rank \(1\).

Complex multiplication

The elliptic curves in class 19950bv do not have complex multiplication.

Modular form 19950.2.a.bv

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.