# Properties

 Label 430950ep Number of curves 8 Conductor 430950 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("430950.ep1")

sage: E.isogeny_class()

## Elliptic curves in class 430950ep

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
430950.ep7 430950ep1 [1, 1, 1, -8856216938, 308890597831031] [2] 1114767360 $$\Gamma_0(N)$$-optimal
430950.ep6 430950ep2 [1, 1, 1, -23479448938, -974034791992969] [2, 2] 2229534720
430950.ep5 430950ep3 [1, 1, 1, -108974520938, -13756221892792969] [2] 3344302080
430950.ep8 430950ep4 [1, 1, 1, 62871439062, -6473895550488969] [2] 4459069440
430950.ep4 430950ep5 [1, 1, 1, -343802048938, -77581106517592969] [2] 4459069440
430950.ep2 430950ep6 [1, 1, 1, -1740435962938, -883762402145248969] [2, 2] 6688604160
430950.ep3 430950ep7 [1, 1, 1, -1737279972438, -887127155104842969] [2] 13377208320
430950.ep1 430950ep8 [1, 1, 1, -27846975025438, -56560760556113998969L] [2] 13377208320

## Rank

sage: E.rank()

The elliptic curves in class 430950ep have rank $$0$$.

## Modular form 430950.2.a.ep

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} - 4q^{7} + q^{8} + q^{9} - q^{12} - 4q^{14} + q^{16} - q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.