Properties

 Label 9240q Number of curves $4$ Conductor $9240$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

Elliptic curves in class 9240q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9240.a4 9240q1 $$[0, -1, 0, 364, 2436]$$ $$20777545136/23059575$$ $$-5903251200$$ $$$$ $$4096$$ $$0.56140$$ $$\Gamma_0(N)$$-optimal
9240.a3 9240q2 $$[0, -1, 0, -2056, 24700]$$ $$939083699236/300155625$$ $$307359360000$$ $$[2, 2]$$ $$8192$$ $$0.90798$$
9240.a2 9240q3 $$[0, -1, 0, -13056, -551700]$$ $$120186986927618/4332064275$$ $$8872067635200$$ $$$$ $$16384$$ $$1.2545$$
9240.a1 9240q4 $$[0, -1, 0, -29776, 1987276]$$ $$1425631925916578/270703125$$ $$554400000000$$ $$$$ $$16384$$ $$1.2545$$

Rank

sage: E.rank()

The elliptic curves in class 9240q have rank $$1$$.

Complex multiplication

The elliptic curves in class 9240q do not have complex multiplication.

Modular form9240.2.a.q

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - q^{7} + q^{9} + q^{11} - 2 q^{13} + q^{15} - 2 q^{17} + O(q^{20})$$ 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels. 