# Properties

 Label 115920.bv Number of curves $2$ Conductor $115920$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 115920.bv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.bv1 115920dt1 $$[0, 0, 0, -743763, -246711278]$$ $$15238420194810961/12619514880$$ $$37681669519441920$$ $$$$ $$1290240$$ $$2.1090$$ $$\Gamma_0(N)$$-optimal
115920.bv2 115920dt2 $$[0, 0, 0, -582483, -356671982]$$ $$-7319577278195281/14169067365600$$ $$-42308608448603750400$$ $$$$ $$2580480$$ $$2.4556$$

## Rank

sage: E.rank()

The elliptic curves in class 115920.bv have rank $$1$$.

## Complex multiplication

The elliptic curves in class 115920.bv do not have complex multiplication.

## Modular form 115920.2.a.bv

sage: E.q_eigenform(10)

$$q - q^{5} + q^{7} + 2 q^{13} + 4 q^{17} - 8 q^{19} + O(q^{20})$$

## 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. 