# Properties

 Label 15680.ca Number of curves $4$ Conductor $15680$ CM no Rank $0$ Graph # Learn more

Show commands for: SageMath
sage: E = EllipticCurve("ca1")

sage: E.isogeny_class()

## Elliptic curves in class 15680.ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.ca1 15680dj3 $$[0, 0, 0, -2561132, -1577596944]$$ $$481927184300808/1225$$ $$4722524979200$$ $$$$ $$147456$$ $$2.0956$$
15680.ca2 15680dj4 $$[0, 0, 0, -209132, -8303344]$$ $$262389836808/144120025$$ $$555600341277900800$$ $$$$ $$147456$$ $$2.0956$$
15680.ca3 15680dj2 $$[0, 0, 0, -160132, -24630144]$$ $$942344950464/1500625$$ $$723136637440000$$ $$[2, 2]$$ $$73728$$ $$1.7490$$
15680.ca4 15680dj1 $$[0, 0, 0, -7007, -620144]$$ $$-5053029696/19140625$$ $$-144120025000000$$ $$$$ $$36864$$ $$1.4024$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 15680.2.a.ca

sage: E.q_eigenform(10)

$$q + q^{5} - 3q^{9} - 2q^{13} - 2q^{17} - 8q^{19} + O(q^{20})$$ ## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 