# Properties

 Label 3136.y Number of curves $2$ Conductor $3136$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("y1")

E.isogeny_class()

## Elliptic curves in class 3136.y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3136.y1 3136z2 $$[0, -1, 0, -1633, -13887]$$ $$125000/49$$ $$188900999168$$ $$[2]$$ $$3072$$ $$0.86233$$
3136.y2 3136z1 $$[0, -1, 0, 327, -1735]$$ $$8000/7$$ $$-3373232128$$ $$[2]$$ $$1536$$ $$0.51575$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3136.y have rank $$1$$.

## Complex multiplication

The elliptic curves in class 3136.y do not have complex multiplication.

## Modular form3136.2.a.y

sage: E.q_eigenform(10)

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

## 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.