# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("el1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.el

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.el1 115920by2 $$[0, 0, 0, -9147, -335414]$$ $$56689453298/253575$$ $$378585446400$$ $$[2]$$ $$196608$$ $$1.0735$$
115920.el2 115920by1 $$[0, 0, 0, -867, 754]$$ $$96550276/55545$$ $$41464120320$$ $$[2]$$ $$98304$$ $$0.72694$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.el

sage: E.q_eigenform(10)

$$q + q^{5} + q^{7} - 2 q^{11} + 6 q^{13} - 2 q^{19} + O(q^{20})$$

## 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.