Properties

 Label 7728.q Number of curves $2$ Conductor $7728$ CM no Rank $1$ Graph Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 7728.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7728.q1 7728e2 $$[0, 1, 0, -30728, 2061972]$$ $$1566789944863250/925924041$$ $$1896292435968$$ $$$$ $$21504$$ $$1.3005$$
7728.q2 7728e1 $$[0, 1, 0, -1568, 44100]$$ $$-416618810500/598934007$$ $$-613308423168$$ $$$$ $$10752$$ $$0.95392$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 7728.q have rank $$1$$.

Complex multiplication

The elliptic curves in class 7728.q do not have complex multiplication.

Modular form7728.2.a.q

sage: E.q_eigenform(10)

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