# Properties

 Label 350064c Number of curves $2$ Conductor $350064$ CM no Rank $2$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 350064c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350064.c1 350064c1 $$[0, 0, 0, -13467, -428470]$$ $$90458382169/25788048$$ $$77002698719232$$ $$[2]$$ $$1228800$$ $$1.3712$$ $$\Gamma_0(N)$$-optimal
350064.c2 350064c2 $$[0, 0, 0, 35493, -2827510]$$ $$1656015369191/2114999172$$ $$-6315353687605248$$ $$[2]$$ $$2457600$$ $$1.7178$$

## Rank

sage: E.rank()

The elliptic curves in class 350064c have rank $$2$$.

## Complex multiplication

The elliptic curves in class 350064c do not have complex multiplication.

## Modular form 350064.2.a.c

sage: E.q_eigenform(10)

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

## 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 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.