# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("ei1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.ei

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.ei1 115920ev1 $$[0, 0, 0, -32952, -2301329]$$ $$339251313639424/173578125$$ $$2024615250000$$ $$$$ $$221184$$ $$1.3130$$ $$\Gamma_0(N)$$-optimal
115920.ei2 115920ev2 $$[0, 0, 0, -27327, -3112454]$$ $$-12092945312464/15426235125$$ $$-2878905703968000$$ $$$$ $$442368$$ $$1.6595$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.ei

sage: E.q_eigenform(10)

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