Properties

 Label 369600jn Number of curves $2$ Conductor $369600$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("jn1")

sage: E.isogeny_class()

Elliptic curves in class 369600jn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
369600.jn2 369600jn1 [0, -1, 0, -894033, -380738313] [] 11520000 $$\Gamma_0(N)$$-optimal
369600.jn1 369600jn2 [0, -1, 0, -2679033, 31909386687] [] 57600000

Rank

sage: E.rank()

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

Complex multiplication

The elliptic curves in class 369600jn do not have complex multiplication.

Modular form 369600.2.a.jn

sage: E.q_eigenform(10)

$$q - q^{3} + q^{7} + q^{9} + q^{11} - 6q^{13} + 7q^{17} - 5q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.