# Properties

 Label 324870.fb Number of curves 4 Conductor 324870 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("324870.fb1")

sage: E.isogeny_class()

## Elliptic curves in class 324870.fb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
324870.fb1 324870fb4 [1, 0, 0, -3754381, -2795530375]  13271040
324870.fb2 324870fb3 [1, 0, 0, -3146781, 2137150665]  13271040
324870.fb3 324870fb2 [1, 0, 0, -314581, -11356255] [2, 2] 6635520
324870.fb4 324870fb1 [1, 0, 0, 77419, -1399455]  3317760 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 324870.fb have rank $$1$$.

## Modular form 324870.2.a.fb

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} + q^{9} - q^{10} - 4q^{11} + q^{12} - q^{13} - q^{15} + q^{16} + q^{17} + q^{18} - 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 