# Properties

 Label 1344.h Number of curves $4$ Conductor $1344$ CM no Rank $0$ Graph # Related objects

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

E.isogeny_class()

## Elliptic curves in class 1344.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1344.h1 1344k3 $$[0, -1, 0, -897, -10047]$$ $$2438569736/21$$ $$688128$$ $$$$ $$512$$ $$0.28794$$
1344.h2 1344k2 $$[0, -1, 0, -57, -135]$$ $$5088448/441$$ $$1806336$$ $$[2, 2]$$ $$256$$ $$-0.058633$$
1344.h3 1344k1 $$[0, -1, 0, -12, 18]$$ $$3241792/567$$ $$36288$$ $$$$ $$128$$ $$-0.40521$$ $$\Gamma_0(N)$$-optimal
1344.h4 1344k4 $$[0, -1, 0, 63, -735]$$ $$830584/7203$$ $$-236027904$$ $$$$ $$512$$ $$0.28794$$

## Rank

sage: E.rank()

The elliptic curves in class 1344.h have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1344.h do not have complex multiplication.

## Modular form1344.2.a.h

sage: E.q_eigenform(10)

$$q - q^{3} + 2 q^{5} - q^{7} + q^{9} + 4 q^{11} + 6 q^{13} - 2 q^{15} - 2 q^{17} - 4 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 