Properties

 Label 7350g Number of curves $6$ Conductor $7350$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7350.p1")

sage: E.isogeny_class()

Elliptic curves in class 7350g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7350.p6 7350g1 [1, 1, 0, 12225, 733125] [2] 36864 $$\Gamma_0(N)$$-optimal
7350.p5 7350g2 [1, 1, 0, -85775, 7495125] [2, 2] 73728
7350.p4 7350g3 [1, 1, 0, -453275, -111207375] [2] 147456
7350.p2 7350g4 [1, 1, 0, -1286275, 560925625] [2, 2] 147456
7350.p1 7350g5 [1, 1, 0, -20580025, 35926369375] [2] 294912
7350.p3 7350g6 [1, 1, 0, -1200525, 639043875] [2] 294912

Rank

sage: E.rank()

The elliptic curves in class 7350g have rank $$0$$.

Modular form7350.2.a.p

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} + 4q^{11} - q^{12} - 2q^{13} + q^{16} + 2q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

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 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.