Properties

 Label 92400.hi Number of curves $2$ Conductor $92400$ CM no Rank $0$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("hi1")

sage: E.isogeny_class()

Elliptic curves in class 92400.hi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.hi1 92400gz2 $$[0, 1, 0, -10716133, 255264377363]$$ $$-2126464142970105856/438611057788643355$$ $$-28071107698473174720000000$$ $$[]$$ $$28800000$$ $$3.5624$$
92400.hi2 92400gz1 $$[0, 1, 0, -3576133, -3049482637]$$ $$-79028701534867456/16987307596875$$ $$-1087187686200000000000$$ $$[]$$ $$5760000$$ $$2.7576$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 92400.hi have rank $$0$$.

Complex multiplication

The elliptic curves in class 92400.hi do not have complex multiplication.

Modular form 92400.2.a.hi

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 LMFDB 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 LMFDB labels.