Properties

 Label 62400z Number of curves $6$ Conductor $62400$ CM no Rank $2$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("62400.cm1")

sage: E.isogeny_class()

Elliptic curves in class 62400z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
62400.cm6 62400z1 [0, -1, 0, 23967, 563937] [2] 294912 $$\Gamma_0(N)$$-optimal
62400.cm5 62400z2 [0, -1, 0, -104033, 4787937] [2, 2] 589824
62400.cm3 62400z3 [0, -1, 0, -904033, -327212063] [2, 2] 1179648
62400.cm2 62400z4 [0, -1, 0, -1352033, 605075937] [2] 1179648
62400.cm4 62400z5 [0, -1, 0, -184033, -834812063] [4] 2359296
62400.cm1 62400z6 [0, -1, 0, -14424033, -21080412063] [2] 2359296

Rank

sage: E.rank()

The elliptic curves in class 62400z have rank $$2$$.

Modular form 62400.2.a.cm

sage: E.q_eigenform(10)

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.