# Properties

 Label 4650.b Number of curves $2$ Conductor $4650$ CM no Rank $1$ Graph

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 4650.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4650.b1 4650m2 $$[1, 1, 0, -35700, 7794000]$$ $$-12882119799145/59982446592$$ $$-23430643200000000$$ $$[]$$ $$36000$$ $$1.8258$$
4650.b2 4650m1 $$[1, 1, 0, -2375, -71475]$$ $$-2372030262025/2061298872$$ $$-1288311795000$$ $$[]$$ $$7200$$ $$1.0210$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4650.b have rank $$1$$.

## Complex multiplication

The elliptic curves in class 4650.b do not have complex multiplication.

## Modular form4650.2.a.b

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.