Properties

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

Related objects

Show commands: SageMath
sage: E = EllipticCurve("iq1")

sage: E.isogeny_class()

Elliptic curves in class 369600.iq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.iq1 369600iq1 $$[0, -1, 0, -36008, 2481762]$$ $$5163364362304/352983015$$ $$352983015000000$$ $$[2]$$ $$1720320$$ $$1.5398$$ $$\Gamma_0(N)$$-optimal
369600.iq2 369600iq2 $$[0, -1, 0, 31367, 10634137]$$ $$53327207744/795685275$$ $$-50923857600000000$$ $$[2]$$ $$3440640$$ $$1.8864$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form 369600.2.a.iq

sage: E.q_eigenform(10)

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

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.