# Properties

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

# Related objects

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)

$$q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} - 2q^{11} + 6q^{13} + q^{16} - 6q^{17} + O(q^{20})$$

## 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.