# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("cd1")

sage: E.isogeny_class()

## Elliptic curves in class 115920cd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.f1 115920cd1 $$[0, 0, 0, -21843, 1059858]$$ $$14295828483/2254000$$ $$181721014272000$$ $$[2]$$ $$331776$$ $$1.4589$$ $$\Gamma_0(N)$$-optimal
115920.f2 115920cd2 $$[0, 0, 0, 38637, 5886162]$$ $$79119341757/231437500$$ $$-18658854144000000$$ $$[2]$$ $$663552$$ $$1.8055$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.cd

sage: E.q_eigenform(10)

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

## 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.