Properties

Label 101430.bv
Number of curves $2$
Conductor $101430$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 101430.bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101430.bv1 101430m1 \([1, -1, 0, -2172631344, -16296617550592]\) \(489781415227546051766883/233890092903563264000\) \(541615842234042702247231488000\) \([2]\) \(148635648\) \(4.3993\) \(\Gamma_0(N)\)-optimal
101430.bv2 101430m2 \([1, -1, 0, 7798343376, -123957219992320]\) \(22649115256119592694355357/15973509811739648000000\) \(-36989621333325446513366016000000\) \([2]\) \(297271296\) \(4.7458\)  

Rank

sage: E.rank()
 

The elliptic curves in class 101430.bv have rank \(1\).

Complex multiplication

The elliptic curves in class 101430.bv do not have complex multiplication.

Modular form 101430.2.a.bv

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} - 2q^{11} + 6q^{13} + q^{16} - 6q^{17} + O(q^{20})\)  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.