# Properties

 Label 355740.bv Number of curves $4$ Conductor $355740$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 355740.bv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
355740.bv1 355740bv4 $$[0, -1, 0, -1482228260, -21963976884408]$$ $$6749703004355978704/5671875$$ $$302629295889228000000$$ $$[2]$$ $$74649600$$ $$3.6655$$
355740.bv2 355740bv3 $$[0, -1, 0, -92618885, -343322540658]$$ $$-26348629355659264/24169921875$$ $$-80600842300042968750000$$ $$[2]$$ $$37324800$$ $$3.3189$$
355740.bv3 355740bv2 $$[0, -1, 0, -18713900, -28685914200]$$ $$13584145739344/1195803675$$ $$63803455504044294931200$$ $$[2]$$ $$24883200$$ $$3.1161$$
355740.bv4 355740bv1 $$[0, -1, 0, 1296475, -2088123750]$$ $$72268906496/606436875$$ $$-2022320269779766110000$$ $$[2]$$ $$12441600$$ $$2.7696$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 355740.bv have rank $$1$$.

## Complex multiplication

The elliptic curves in class 355740.bv do not have complex multiplication.

## Modular form 355740.2.a.bv

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{9} + 2q^{13} - q^{15} + 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.