# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("ce1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.ce

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.ce1 115920cg1 $$[0, 0, 0, -597483, -173265318]$$ $$292583028222603/8456021875$$ $$681737742604800000$$ $$$$ $$1658880$$ $$2.1999$$ $$\Gamma_0(N)$$-optimal
115920.ce2 115920cg2 $$[0, 0, 0, 143397, -574674102]$$ $$4044759171237/1771943359375$$ $$-142856852040000000000$$ $$$$ $$3317760$$ $$2.5465$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.ce

sage: E.q_eigenform(10)

$$q - q^{5} + q^{7} + 4 q^{11} + 4 q^{13} - 6 q^{17} - 4 q^{19} + O(q^{20})$$ ## 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. 