# Properties

 Label 2646.h Number of curves $2$ Conductor $2646$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 2646.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2646.h1 2646i1 $$[1, -1, 0, -8682, 320228]$$ $$-637875/16$$ $$-1815497249328$$ $$$$ $$6048$$ $$1.1366$$ $$\Gamma_0(N)$$-optimal
2646.h2 2646i2 $$[1, -1, 0, 37623, 1329677]$$ $$5767125/4096$$ $$-4182905662451712$$ $$[]$$ $$18144$$ $$1.6859$$

## Rank

sage: E.rank()

The elliptic curves in class 2646.h have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2646.h do not have complex multiplication.

## Modular form2646.2.a.h

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{8} + 6q^{11} + 5q^{13} + q^{16} + 6q^{17} - 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 