Properties

 Label 433200fl Number of curves $4$ Conductor $433200$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("433200.fl1")

sage: E.isogeny_class()

Elliptic curves in class 433200fl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
433200.fl4 433200fl1 [0, -1, 0, -1447008, 1143712512] [2] 19906560 $$\Gamma_0(N)$$-optimal*
433200.fl3 433200fl2 [0, -1, 0, -27439008, 55311040512] [2, 2] 39813120 $$\Gamma_0(N)$$-optimal*
433200.fl1 433200fl3 [0, -1, 0, -438979008, 3540231760512] [4] 79626240 $$\Gamma_0(N)$$-optimal*
433200.fl2 433200fl4 [0, -1, 0, -31771008, 36683440512] [2] 79626240
*optimality has not been proved rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 433200fl1.

Rank

sage: E.rank()

The elliptic curves in class 433200fl have rank $$1$$.

Modular form 433200.2.a.fl

sage: E.q_eigenform(10)

$$q - q^{3} + 4q^{7} + q^{9} + 4q^{11} - 2q^{13} + 2q^{17} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.