# Properties

 Label 435344h Number of curves $2$ Conductor $435344$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 435344h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
435344.h2 435344h1 $$[0, 1, 0, -4788, -165476]$$ $$-9826000/3703$$ $$-4575660474112$$ $$[2]$$ $$614400$$ $$1.1391$$ $$\Gamma_0(N)$$-optimal*
435344.h1 435344h2 $$[0, 1, 0, -82528, -9152220]$$ $$12576878500/1127$$ $$5570369272832$$ $$[2]$$ $$1228800$$ $$1.4857$$ $$\Gamma_0(N)$$-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 435344h1.

## Rank

sage: E.rank()

The elliptic curves in class 435344h have rank $$1$$.

## Complex multiplication

The elliptic curves in class 435344h do not have complex multiplication.

## Modular form 435344.2.a.h

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.