# Properties

 Label 364650.ec Number of curves $2$ Conductor $364650$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("ec1")

sage: E.isogeny_class()

## Elliptic curves in class 364650.ec

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
364650.ec1 364650ec1 $$[1, 1, 1, -2338, -31969]$$ $$90458382169/25788048$$ $$402938250000$$ $$$$ $$512000$$ $$0.93347$$ $$\Gamma_0(N)$$-optimal
364650.ec2 364650ec2 $$[1, 1, 1, 6162, -201969]$$ $$1656015369191/2114999172$$ $$-33046862062500$$ $$$$ $$1024000$$ $$1.2800$$

## Rank

sage: E.rank()

The elliptic curves in class 364650.ec have rank $$0$$.

## Complex multiplication

The elliptic curves in class 364650.ec do not have complex multiplication.

## Modular form 364650.2.a.ec

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} + q^{11} - q^{12} + q^{13} + q^{16} - q^{17} + q^{18} + 2q^{19} + O(q^{20})$$ ## 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 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. 