# Properties

 Label 308550.jf Number of curves 6 Conductor 308550 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("308550.jf1")

sage: E.isogeny_class()

## Elliptic curves in class 308550.jf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
308550.jf1 308550jf5 [1, 0, 0, -883723563, 10110389996367] [2] 141557760
308550.jf2 308550jf3 [1, 0, 0, -60167313, 128064690117] [2, 2] 70778880
308550.jf3 308550jf2 [1, 0, 0, -22354813, -39104372383] [2, 2] 35389440
308550.jf4 308550jf1 [1, 0, 0, -22112813, -40025182383] [2] 17694720 $$\Gamma_0(N)$$-optimal
308550.jf5 308550jf4 [1, 0, 0, 11585687, -147340626883] [2] 70778880
308550.jf6 308550jf6 [1, 0, 0, 158388937, 844710633867] [2] 141557760

## Rank

sage: E.rank()

The elliptic curves in class 308550.jf have rank $$1$$.

## Modular form 308550.2.a.jf

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.