Properties

 Label 960o Number of curves 8 Conductor 960 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("960.p1")

sage: E.isogeny_class()

Elliptic curves in class 960o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
960.p8 960o1 [0, 1, 0, 95, -1057] [2] 384 $$\Gamma_0(N)$$-optimal
960.p6 960o2 [0, 1, 0, -1185, -14625] [2, 2] 768
960.p7 960o3 [0, 1, 0, -865, 31775] [2] 1152
960.p4 960o4 [0, 1, 0, -18465, -971937] [2] 1536
960.p5 960o5 [0, 1, 0, -4385, 94815] [4] 1536
960.p3 960o6 [0, 1, 0, -21345, 1190943] [2, 2] 2304
960.p2 960o7 [0, 1, 0, -29025, 249375] [2] 4608
960.p1 960o8 [0, 1, 0, -341345, 76646943] [4] 4608

Rank

sage: E.rank()

The elliptic curves in class 960o have rank $$0$$.

Modular form960.2.a.p

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + 4q^{7} + q^{9} - 2q^{13} + q^{15} + 6q^{17} - 4q^{19} + O(q^{20})$$

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 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.