Properties

 Label 369600pg Number of curves $6$ Conductor $369600$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("369600.pg1")

sage: E.isogeny_class()

Elliptic curves in class 369600pg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
369600.pg4 369600pg1 [0, 1, 0, -424033, -106419937] [2] 3145728 $$\Gamma_0(N)$$-optimal
369600.pg3 369600pg2 [0, 1, 0, -432033, -102203937] [2, 2] 6291456
369600.pg2 369600pg3 [0, 1, 0, -1400033, 516348063] [2, 2] 12582912
369600.pg5 369600pg4 [0, 1, 0, 407967, -450803937] [2] 12582912
369600.pg1 369600pg5 [0, 1, 0, -21200033, 37562148063] [2] 25165824
369600.pg6 369600pg6 [0, 1, 0, 2911967, 3073364063] [2] 25165824

Rank

sage: E.rank()

The elliptic curves in class 369600pg have rank $$0$$.

Modular form 369600.2.a.pg

sage: E.q_eigenform(10)

$$q + q^{3} - q^{7} + q^{9} + q^{11} - 2q^{13} + 6q^{17} - 4q^{19} + O(q^{20})$$

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.