Properties

 Label 7800.t Number of curves $4$ Conductor $7800$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("t1")

sage: E.isogeny_class()

Elliptic curves in class 7800.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7800.t1 7800d4 $$[0, 1, 0, -192408, 32342688]$$ $$49235161015876/137109375$$ $$2193750000000000$$ $$$$ $$36864$$ $$1.8162$$
7800.t2 7800d3 $$[0, 1, 0, -179408, -29199312]$$ $$39914580075556/172718325$$ $$2763493200000000$$ $$$$ $$36864$$ $$1.8162$$
7800.t3 7800d2 $$[0, 1, 0, -16908, 50688]$$ $$133649126224/77000625$$ $$308002500000000$$ $$[2, 2]$$ $$18432$$ $$1.4697$$
7800.t4 7800d1 $$[0, 1, 0, 4217, 8438]$$ $$33165879296/19278675$$ $$-4819668750000$$ $$$$ $$9216$$ $$1.1231$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 7800.t have rank $$0$$.

Complex multiplication

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

Modular form7800.2.a.t

sage: E.q_eigenform(10)

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels. 