# Properties

 Label 15680.dm Number of curves $2$ Conductor $15680$ CM no Rank $0$ Graph # Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 15680.dm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.dm1 15680dr2 $$[0, -1, 0, -10145, -679615]$$ $$-8990558521/10485760$$ $$-134690174402560$$ $$[]$$ $$48384$$ $$1.4052$$
15680.dm2 15680dr1 $$[0, -1, 0, 1055, 17025]$$ $$10100279/16000$$ $$-205520896000$$ $$[]$$ $$16128$$ $$0.85594$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 15680.dm have rank $$0$$.

## Complex multiplication

The elliptic curves in class 15680.dm do not have complex multiplication.

## Modular form 15680.2.a.dm

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{5} + q^{9} + 3q^{11} - q^{13} + 2q^{15} + 6q^{17} + q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 