# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cl1")

sage: E.isogeny_class()

## Elliptic curves in class 115920cl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.cw1 115920cl1 $$[0, 0, 0, -78825627, 112624801354]$$ $$489781415227546051766883/233890092903563264000$$ $$25866373154390868492288000$$ $$[2]$$ $$24772608$$ $$3.5701$$ $$\Gamma_0(N)$$-optimal
115920.cw2 115920cl2 $$[0, 0, 0, 282933093, 856617784906]$$ $$22649115256119592694355357/15973509811739648000000$$ $$-1766542397099911151616000000$$ $$[2]$$ $$49545216$$ $$3.9167$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.cl

sage: E.q_eigenform(10)

$$q + q^{5} - q^{7} - 2q^{11} - 6q^{13} - 6q^{17} + O(q^{20})$$

## 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 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.