# Properties

 Label 322050.bv Number of curves $2$ Conductor $322050$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 322050.bv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
322050.bv1 322050bv1 $$[1, 0, 0, -12372088, -9881910208]$$ $$13403946614821979039929/5057590268826067968$$ $$79024847950407312000000$$ $$$$ $$50585600$$ $$3.0932$$ $$\Gamma_0(N)$$-optimal
322050.bv2 322050bv2 $$[1, 0, 0, 38703912, -70509122208]$$ $$410363075617640914325831/374944243169850027552$$ $$-5858503799528906680500000$$ $$$$ $$101171200$$ $$3.4398$$

## Rank

sage: E.rank()

The elliptic curves in class 322050.bv have rank $$0$$.

## Complex multiplication

The elliptic curves in class 322050.bv do not have complex multiplication.

## Modular form 322050.2.a.bv

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + 4q^{7} + q^{8} + q^{9} + q^{12} + 4q^{14} + q^{16} + 6q^{17} + q^{18} + q^{19} + O(q^{20})$$ ## 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. 