# Properties

 Label 369600uc Number of curves 6 Conductor 369600 CM no Rank 0 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("369600.uc1")

sage: E.isogeny_class()

## Elliptic curves in class 369600uc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
369600.uc4 369600uc1 [0, 1, 0, -54433, -4904737] [2] 1310720 $$\Gamma_0(N)$$-optimal
369600.uc3 369600uc2 [0, 1, 0, -62433, -3376737] [2, 2] 2621440
369600.uc2 369600uc3 [0, 1, 0, -454433, 115399263] [2, 2] 5242880
369600.uc6 369600uc4 [0, 1, 0, 201567, -24232737] [2] 5242880
369600.uc1 369600uc5 [0, 1, 0, -7230433, 7480911263] [2] 10485760
369600.uc5 369600uc6 [0, 1, 0, 49567, 357823263] [2] 10485760

## Rank

sage: E.rank()

The elliptic curves in class 369600uc have rank $$0$$.

## Modular form 369600.2.a.uc

sage: E.q_eigenform(10)

$$q + q^{3} + q^{7} + q^{9} - q^{11} + 6q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.