# Properties

 Label 5070.w Number of curves 8 Conductor 5070 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("5070.w1")

sage: E.isogeny_class()

## Elliptic curves in class 5070.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5070.w1 5070v7 [1, 0, 0, -901365, -329456583] [2] 55296
5070.w2 5070v8 [1, 0, 0, -76645, -1117975] [2] 55296
5070.w3 5070v6 [1, 0, 0, -56365, -5145583] [2, 2] 27648
5070.w4 5070v5 [1, 0, 0, -48760, 4140122] [2] 18432
5070.w5 5070v4 [1, 0, 0, -11580, -414090] [2] 18432
5070.w6 5070v2 [1, 0, 0, -3130, 60800] [2, 2] 9216
5070.w7 5070v3 [1, 0, 0, -2285, -137775] [2] 13824
5070.w8 5070v1 [1, 0, 0, 250, 4692] [2] 4608 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 5070.w have rank $$0$$.

## Modular form5070.2.a.w

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + 4q^{7} + q^{8} + q^{9} + q^{10} + q^{12} + 4q^{14} + q^{15} + q^{16} + 6q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.