# Properties

 Label 115920cr Number of curves $2$ Conductor $115920$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("cr1")

sage: E.isogeny_class()

## Elliptic curves in class 115920cr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.fe2 115920cr1 $$[0, 0, 0, -226827, -40941126]$$ $$16008724040427/282741760$$ $$22795084030279680$$ $$[2]$$ $$921600$$ $$1.9350$$ $$\Gamma_0(N)$$-optimal
115920.fe1 115920cr2 $$[0, 0, 0, -3613707, -2644097094]$$ $$64733826967442667/20736800$$ $$1671833331302400$$ $$[2]$$ $$1843200$$ $$2.2816$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.cr

sage: E.q_eigenform(10)

$$q + q^{5} + q^{7} + 4 q^{11} + 4 q^{13} + 4 q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.