# Properties

 Label 3450.b Number of curves $2$ Conductor $3450$ CM no Rank $0$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 3450.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3450.b1 3450c2 $$[1, 1, 0, -98125, -11871875]$$ $$6687281588245201/165600$$ $$2587500000$$ $$[2]$$ $$11520$$ $$1.3246$$
3450.b2 3450c1 $$[1, 1, 0, -6125, -187875]$$ $$-1626794704081/8125440$$ $$-126960000000$$ $$[2]$$ $$5760$$ $$0.97805$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3450.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3450.b do not have complex multiplication.

## Modular form3450.2.a.b

sage: E.q_eigenform(10)

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

## 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 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.