# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("dg1")

sage: E.isogeny_class()

## Elliptic curves in class 115920dg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.c1 115920dg1 $$[0, 0, 0, -35283, 2435218]$$ $$1626794704081/83462400$$ $$249217391001600$$ $$$$ $$589824$$ $$1.5203$$ $$\Gamma_0(N)$$-optimal
115920.c2 115920dg2 $$[0, 0, 0, 22317, 9612178]$$ $$411664745519/13605414480$$ $$-40625549950648320$$ $$$$ $$1179648$$ $$1.8669$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.dg

sage: E.q_eigenform(10)

$$q - q^{5} - q^{7} - 6q^{11} - 6q^{17} + 8q^{19} + O(q^{20})$$ ## 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. 