# Properties

 Label 436800.mr Number of curves 8 Conductor 436800 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("436800.mr1")

sage: E.isogeny_class()

## Elliptic curves in class 436800.mr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
436800.mr1 436800mr8 [0, 1, 0, -64304728033, -6276448294455937] [u'2'] 509607936
436800.mr2 436800mr6 [0, 1, 0, -4019048033, -98070379655937] [u'2', u'2'] 254803968
436800.mr3 436800mr7 [0, 1, 0, -3969656033, -100598212823937] [u'2'] 509607936
436800.mr4 436800mr5 [0, 1, 0, -794248033, -8601647655937] [u'2'] 169869312
436800.mr5 436800mr3 [0, 1, 0, -254280033, -1492786151937] [u'2'] 127401984
436800.mr6 436800mr2 [0, 1, 0, -66248033, -36727655937] [u'2', u'2'] 84934656
436800.mr7 436800mr1 [0, 1, 0, -41160033, 101080728063] [u'2'] 42467328 $$\Gamma_0(N)$$-optimal
436800.mr8 436800mr4 [0, 1, 0, 260343967, -291142823937] [u'2'] 169869312

## Rank

sage: E.rank()

The elliptic curves in class 436800.mr have rank $$1$$.

## Modular form 436800.2.a.mr

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.