Properties

 Label 79350.k Number of curves $6$ Conductor $79350$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("79350.k1")

sage: E.isogeny_class()

Elliptic curves in class 79350.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
79350.k1 79350e4 [1, 1, 0, -1460040275, -21473739057375] [2] 19464192
79350.k2 79350e6 [1, 1, 0, -341602025, 2081475474375] [2] 38928384
79350.k3 79350e3 [1, 1, 0, -93633275, -317126244375] [2, 2] 19464192
79350.k4 79350e2 [1, 1, 0, -91252775, -335553694875] [2, 2] 9732096
79350.k5 79350e1 [1, 1, 0, -5554775, -5530696875] [2] 4866048 $$\Gamma_0(N)$$-optimal
79350.k6 79350e5 [1, 1, 0, 116247475, -1536323521125] [2] 38928384

Rank

sage: E.rank()

The elliptic curves in class 79350.k have rank $$0$$.

Modular form 79350.2.a.k

sage: E.q_eigenform(10)

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.