# Properties

 Label 384.h Number of curves $2$ Conductor $384$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 384.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
384.h1 384e2 [0, 1, 0, -141, -693] [2] 96
384.h2 384e1 [0, 1, 0, -6, -18] [2] 48 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 384.h have rank $$0$$.

## Complex multiplication

The elliptic curves in class 384.h do not have complex multiplication.

## Modular form384.2.a.h

sage: E.q_eigenform(10)

$$q + q^{3} + 4q^{5} + 2q^{7} + q^{9} - 4q^{11} - 2q^{13} + 4q^{15} - 2q^{17} - 8q^{19} + O(q^{20})$$

## 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.