# Properties

 Label 15631c Number of curves $4$ Conductor $15631$ CM no Rank $1$ Graph

# Learn more

Show commands for: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 15631c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15631.a4 15631c1 $$[1, -1, 1, 28631, -2132504]$$ $$22062729659823/29354283343$$ $$-3453502081020607$$ $$[4]$$ $$64512$$ $$1.6673$$ $$\Gamma_0(N)$$-optimal
15631.a3 15631c2 $$[1, -1, 1, -177414, -20758972]$$ $$5249244962308257/1448621666569$$ $$170428890450176281$$ $$[2, 2]$$ $$129024$$ $$2.0139$$
15631.a1 15631c3 $$[1, -1, 1, -2614429, -1626264454]$$ $$16798320881842096017/2132227789307$$ $$250854467184179243$$ $$[2]$$ $$258048$$ $$2.3605$$
15631.a2 15631c4 $$[1, -1, 1, -1037119, 390180018]$$ $$1048626554636928177/48569076788309$$ $$5714103315067765541$$ $$[2]$$ $$258048$$ $$2.3605$$

## Rank

sage: E.rank()

The elliptic curves in class 15631c have rank $$1$$.

## Complex multiplication

The elliptic curves in class 15631c do not have complex multiplication.

## Modular form 15631.2.a.c

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} + 2q^{5} + 3q^{8} - 3q^{9} - 2q^{10} - q^{11} - 6q^{13} - q^{16} + 2q^{17} + 3q^{18} + 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.