# Properties

 Label 64400ci Number of curves $2$ Conductor $64400$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("ci1")

sage: E.isogeny_class()

## Elliptic curves in class 64400ci

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.h2 64400ci1 $$[0, 1, 0, 27, 58]$$ $$1048576/1127$$ $$-2254000$$ $$$$ $$11520$$ $$-0.094350$$ $$\Gamma_0(N)$$-optimal
64400.h1 64400ci2 $$[0, 1, 0, -148, 408]$$ $$11279504/3703$$ $$118496000$$ $$$$ $$23040$$ $$0.25222$$

## Rank

sage: E.rank()

The elliptic curves in class 64400ci have rank $$0$$.

## Complex multiplication

The elliptic curves in class 64400ci do not have complex multiplication.

## Modular form 64400.2.a.ci

sage: E.q_eigenform(10)

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