# Properties

 Label 3136.w Number of curves $2$ Conductor $3136$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("w1")

E.isogeny_class()

## Elliptic curves in class 3136.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3136.w1 3136j2 $$[0, -1, 0, -7905, 269921]$$ $$3543122/49$$ $$755603996672$$ $$$$ $$6144$$ $$1.0849$$
3136.w2 3136j1 $$[0, -1, 0, -65, 11201]$$ $$-4/7$$ $$-53971714048$$ $$$$ $$3072$$ $$0.73829$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3136.w have rank $$0$$.

## Complex multiplication

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

## Modular form3136.2.a.w

sage: E.q_eigenform(10)

$$q + 2 q^{3} - 4 q^{5} + q^{9} - 8 q^{15} + 2 q^{17} - 2 q^{19} + O(q^{20})$$

## 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. 