Properties

 Label 21294.bu Number of curves $6$ Conductor $21294$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("21294.bu1")

sage: E.isogeny_class()

Elliptic curves in class 21294.bu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
21294.bu1 21294cm4 [1, -1, 1, -2044256, -1124484825] [2] 245760
21294.bu2 21294cm6 [1, -1, 1, -1390226, 625212735] [2] 491520
21294.bu3 21294cm3 [1, -1, 1, -158216, -8533209] [2, 2] 245760
21294.bu4 21294cm2 [1, -1, 1, -127796, -17537529] [2, 2] 122880
21294.bu5 21294cm1 [1, -1, 1, -6116, -404985] [2] 61440 $$\Gamma_0(N)$$-optimal
21294.bu6 21294cm5 [1, -1, 1, 587074, -66367713] [2] 491520

Rank

sage: E.rank()

The elliptic curves in class 21294.bu have rank $$0$$.

Modular form 21294.2.a.bu

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - 2q^{5} + q^{7} + q^{8} - 2q^{10} - 4q^{11} + q^{14} + q^{16} - 2q^{17} + 4q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.