# Properties

 Label 298816.h Number of curves $2$ Conductor $298816$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 298816.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
298816.h1 298816h2 $$[0, 1, 0, -23553, 23551]$$ $$5512402554625/3188422748$$ $$835825892851712$$ $$$$ $$1032192$$ $$1.5528$$
298816.h2 298816h1 $$[0, 1, 0, 5887, 5887]$$ $$86058173375/49827568$$ $$-13061997985792$$ $$$$ $$516096$$ $$1.2062$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 298816.h have rank $$0$$.

## Complex multiplication

The elliptic curves in class 298816.h do not have complex multiplication.

## Modular form 298816.2.a.h

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{7} + q^{9} + 4q^{11} + 2q^{13} + 4q^{17} + O(q^{20})$$ ## 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. 