# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("dm1")

sage: E.isogeny_class()

## Elliptic curves in class 115920.dm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.dm1 115920ck1 $$[0, 0, 0, -183627, -29710854]$$ $$8493409990827/185150000$$ $$14927083315200000$$ $$[2]$$ $$737280$$ $$1.8918$$ $$\Gamma_0(N)$$-optimal
115920.dm2 115920ck2 $$[0, 0, 0, 15093, -90638406]$$ $$4716275733/44023437500$$ $$-3549238560000000000$$ $$[2]$$ $$1474560$$ $$2.2383$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 115920.2.a.dm

sage: E.q_eigenform(10)

$$q + q^{5} - q^{7} + 2 q^{11} + 2 q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})$$

## 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.