# Properties

 Label 350.a Number of curves $2$ Conductor $350$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 350.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350.a1 350c2 $$[1, 1, 0, -45, -185]$$ $$-417267265/235298$$ $$-5882450$$ $$[]$$ $$72$$ $$0.0021345$$
350.a2 350c1 $$[1, 1, 0, 5, 5]$$ $$397535/392$$ $$-9800$$ $$[]$$ $$24$$ $$-0.54717$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 350.a have rank $$1$$.

## Complex multiplication

The elliptic curves in class 350.a do not have complex multiplication.

## Modular form350.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} - 2q^{9} + 3q^{11} - q^{12} - 2q^{13} + q^{14} + q^{16} - 3q^{17} + 2q^{18} - 7q^{19} + O(q^{20})$$ ## 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. 