Properties

 Label 7440o Number of curves $6$ Conductor $7440$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7440.j1")

sage: E.isogeny_class()

Elliptic curves in class 7440o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7440.j6 7440o1 [0, -1, 0, 960, 64512] [2] 12288 $$\Gamma_0(N)$$-optimal
7440.j5 7440o2 [0, -1, 0, -19520, 998400] [2, 2] 24576
7440.j4 7440o3 [0, -1, 0, -59200, -4302848] [2] 49152
7440.j2 7440o4 [0, -1, 0, -307520, 65740800] [2, 4] 49152
7440.j1 7440o5 [0, -1, 0, -4920320, 4202499840] [4] 98304
7440.j3 7440o6 [0, -1, 0, -302720, 67887360] [4] 98304

Rank

sage: E.rank()

The elliptic curves in class 7440o have rank $$0$$.

Modular form7440.2.a.j

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{9} + 4q^{11} + 6q^{13} - q^{15} + 2q^{17} - 4q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.