Properties

 Label 7800.s Number of curves $2$ Conductor $7800$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("s1")

sage: E.isogeny_class()

Elliptic curves in class 7800.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7800.s1 7800i1 $$[0, 1, 0, -16283, 745938]$$ $$1909913257984/129730653$$ $$32432663250000$$ $$$$ $$19200$$ $$1.3411$$ $$\Gamma_0(N)$$-optimal
7800.s2 7800i2 $$[0, 1, 0, 14092, 3236688]$$ $$77366117936/1172914587$$ $$-4691658348000000$$ $$$$ $$38400$$ $$1.6877$$

Rank

sage: E.rank()

The elliptic curves in class 7800.s have rank $$1$$.

Complex multiplication

The elliptic curves in class 7800.s do not have complex multiplication.

Modular form7800.2.a.s

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} - 2 q^{11} + q^{13} - 2 q^{17} + 8 q^{19} + O(q^{20})$$ 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. 