Properties

 Label 58800.ji Number of curves $6$ Conductor $58800$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("58800.ji1")

sage: E.isogeny_class()

Elliptic curves in class 58800.ji

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
58800.ji1 58800dj6 [0, 1, 0, -12838408, -17709656812] [2] 2359296
58800.ji2 58800dj4 [0, 1, 0, -833408, -254386812] [2, 2] 1179648
58800.ji3 58800dj2 [0, 1, 0, -220908, 35938188] [2, 2] 589824
58800.ji4 58800dj1 [0, 1, 0, -214783, 38241188] [2] 294912 $$\Gamma_0(N)$$-optimal
58800.ji5 58800dj3 [0, 1, 0, 293592, 178969188] [2] 1179648
58800.ji6 58800dj5 [0, 1, 0, 1371592, -1370116812] [2] 2359296

Rank

sage: E.rank()

The elliptic curves in class 58800.ji have rank $$1$$.

Modular form 58800.2.a.ji

sage: E.q_eigenform(10)

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.