# Properties

 Label 3136s Number of curves $4$ Conductor $3136$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("s1")

E.isogeny_class()

## Elliptic curves in class 3136s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3136.p4 3136s1 $$[0, 0, 0, 196, 5488]$$ $$432/7$$ $$-13492928512$$ $$[2]$$ $$1536$$ $$0.62435$$ $$\Gamma_0(N)$$-optimal
3136.p3 3136s2 $$[0, 0, 0, -3724, 82320]$$ $$740772/49$$ $$377801998336$$ $$[2, 2]$$ $$3072$$ $$0.97092$$
3136.p2 3136s3 $$[0, 0, 0, -11564, -378672]$$ $$11090466/2401$$ $$37024595836928$$ $$[2]$$ $$6144$$ $$1.3175$$
3136.p1 3136s4 $$[0, 0, 0, -58604, 5460560]$$ $$1443468546/7$$ $$107943428096$$ $$[2]$$ $$6144$$ $$1.3175$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3136.2.a.s

sage: E.q_eigenform(10)

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

## 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 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.