# Properties

 Label 1152.h Number of curves $2$ Conductor $1152$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1152.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1152.h1 1152g1 $$[0, 0, 0, -21, 34]$$ $$10976$$ $$93312$$ $$$$ $$96$$ $$-0.30712$$ $$\Gamma_0(N)$$-optimal
1152.h2 1152g2 $$[0, 0, 0, 24, 160]$$ $$128$$ $$-11943936$$ $$$$ $$192$$ $$0.039450$$

## Rank

sage: E.rank()

The elliptic curves in class 1152.h have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1152.h do not have complex multiplication.

## Modular form1152.2.a.h

sage: E.q_eigenform(10)

$$q - 2q^{5} + 4q^{7} - 2q^{11} + 2q^{13} + 2q^{17} - 2q^{19} + O(q^{20})$$ ## 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. 