# Properties

 Label 15680.v Number of curves $2$ Conductor $15680$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 15680.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.v1 15680df2 $$[0, 1, 0, -31425, 2133823]$$ $$-5452947409/250$$ $$-157351936000$$ $$[]$$ $$34560$$ $$1.2241$$
15680.v2 15680df1 $$[0, 1, 0, -65, 7615]$$ $$-49/40$$ $$-25176309760$$ $$[]$$ $$11520$$ $$0.67480$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 15680.v have rank $$1$$.

## Complex multiplication

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

## Modular form 15680.2.a.v

sage: E.q_eigenform(10)

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