Properties

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

Related objects

Show commands: SageMath
sage: E = EllipticCurve("rn1")

sage: E.isogeny_class()

Elliptic curves in class 369600.rn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.rn1 369600rn2 $$[0, 1, 0, -90656432833, 2818545808546463]$$ $$160934676078320454012702173/86430430219822569086976$$ $$44252380272549155372531712000000000$$ $$[2]$$ $$3220439040$$ $$5.3391$$
369600.rn2 369600rn1 $$[0, 1, 0, 21737807167, 345535345826463]$$ $$2218712073897830722499107/1384711926834951880704$$ $$-708972506539495362920448000000000$$ $$[2]$$ $$1610219520$$ $$4.9925$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form 369600.2.a.rn

sage: E.q_eigenform(10)

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.