# Properties

 Label 115920i Number of curves $2$ Conductor $115920$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 115920i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.ds1 115920i1 $$[0, 0, 0, -87, 86]$$ $$10536048/5635$$ $$38949120$$ $$$$ $$30720$$ $$0.14774$$ $$\Gamma_0(N)$$-optimal
115920.ds2 115920i2 $$[0, 0, 0, 333, 674]$$ $$147704148/92575$$ $$-2559513600$$ $$$$ $$61440$$ $$0.49432$$

## Rank

sage: E.rank()

The elliptic curves in class 115920i have rank $$0$$.

## Complex multiplication

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

## Modular form 115920.2.a.i

sage: E.q_eigenform(10)

$$q + q^{5} - q^{7} + 4q^{11} + 4q^{13} + 2q^{17} - 4q^{19} + O(q^{20})$$ ## 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. 