# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.i1 115920cw2 $$[0, 0, 0, -106203, -23798]$$ $$44365623586201/25674468750$$ $$76663552896000000$$ $$$$ $$884736$$ $$1.9293$$
115920.i2 115920cw1 $$[0, 0, 0, -73083, -7581782]$$ $$14457238157881/49990500$$ $$149270833152000$$ $$$$ $$442368$$ $$1.5827$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.i

sage: E.q_eigenform(10)

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