# Properties

 Label 64400ca Number of curves $4$ Conductor $64400$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("ca1")

sage: E.isogeny_class()

## Elliptic curves in class 64400ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.m4 64400ca1 $$[0, 1, 0, -736408, -242440812]$$ $$690080604747409/3406760000$$ $$218032640000000000$$ $$$$ $$1437696$$ $$2.1746$$ $$\Gamma_0(N)$$-optimal
64400.m3 64400ca2 $$[0, 1, 0, -1136408, 49559188]$$ $$2535986675931409/1450751712200$$ $$92848109580800000000$$ $$$$ $$2875392$$ $$2.5212$$
64400.m2 64400ca3 $$[0, 1, 0, -4232408, 3175175188]$$ $$131010595463836369/7704101562500$$ $$493062500000000000000$$ $$$$ $$4313088$$ $$2.7239$$
64400.m1 64400ca4 $$[0, 1, 0, -66732408, 209800175188]$$ $$513516182162686336369/1944885031250$$ $$124472642000000000000$$ $$$$ $$8626176$$ $$3.0705$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 64400.2.a.ca

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{7} + q^{9} + 6q^{11} + 4q^{13} - 6q^{17} - 8q^{19} + O(q^{20})$$ ## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 