# Properties

 Label 384.c Number of curves $2$ Conductor $384$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 384.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
384.c1 384b2 $$[0, -1, 0, -13, -11]$$ $$16000/3$$ $$49152$$ $$$$ $$32$$ $$-0.38187$$
384.c2 384b1 $$[0, -1, 0, 2, -2]$$ $$4000/9$$ $$-1152$$ $$$$ $$16$$ $$-0.72845$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form384.2.a.c

sage: E.q_eigenform(10)

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