# Properties

 Label 303450.a Number of curves $2$ Conductor $303450$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 303450.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303450.a1 303450a2 $$[1, 1, 0, -101300, -13172400]$$ $$-7620530425/526848$$ $$-7948018720320000$$ $$[]$$ $$3265920$$ $$1.8019$$
303450.a2 303450a1 $$[1, 1, 0, 7075, -15675]$$ $$2595575/1512$$ $$-22810002705000$$ $$[]$$ $$1088640$$ $$1.2526$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 303450.a have rank $$0$$.

## Complex multiplication

The elliptic curves in class 303450.a do not have complex multiplication.

## Modular form 303450.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} - 6q^{11} - q^{12} - q^{13} + q^{14} + q^{16} - q^{18} - 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 