# Properties

 Label 303450.bc Number of curves $6$ Conductor $303450$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("303450.bc1")

sage: E.isogeny_class()

## Elliptic curves in class 303450.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
303450.bc1 303450bc6 [1, 1, 0, -99116914050, -12010780810048500] [2] 1132462080
303450.bc2 303450bc4 [1, 1, 0, -6206593050, -186920449267500] [2, 2] 566231040
303450.bc3 303450bc5 [1, 1, 0, -2114064050, -429734287366500] [2] 1132462080
303450.bc4 303450bc2 [1, 1, 0, -655481050, 1623069812500] [2, 2] 283115520
303450.bc5 303450bc1 [1, 1, 0, -507513050, 4394954356500] [2] 141557760 $$\Gamma_0(N)$$-optimal
303450.bc6 303450bc3 [1, 1, 0, 2528142950, 12768937436500] [2] 566231040

## Rank

sage: E.rank()

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

## Modular form 303450.2.a.bc

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.