# Properties

 Label 115920dc Number of curves $2$ Conductor $115920$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("dc1")

sage: E.isogeny_class()

## Elliptic curves in class 115920dc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.j1 115920dc1 $$[0, 0, 0, -33123, -1993822]$$ $$1345938541921/203765625$$ $$608440896000000$$ $$[2]$$ $$393216$$ $$1.5608$$ $$\Gamma_0(N)$$-optimal
115920.j2 115920dc2 $$[0, 0, 0, 56877, -10939822]$$ $$6814692748079/21258460125$$ $$-63477421797888000$$ $$[2]$$ $$786432$$ $$1.9074$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.dc

sage: E.q_eigenform(10)

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

## 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.