Properties

 Label 7800.u Number of curves $4$ Conductor $7800$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("u1")

sage: E.isogeny_class()

Elliptic curves in class 7800.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7800.u1 7800t4 $$[0, 1, 0, -145408, 21286688]$$ $$10625310339698/3855735$$ $$123383520000000$$ $$$$ $$36864$$ $$1.6724$$
7800.u2 7800t3 $$[0, 1, 0, -75408, -7833312]$$ $$1481943889298/34543665$$ $$1105397280000000$$ $$$$ $$36864$$ $$1.6724$$
7800.u3 7800t2 $$[0, 1, 0, -10408, 226688]$$ $$7793764996/3080025$$ $$49280400000000$$ $$[2, 2]$$ $$18432$$ $$1.3258$$
7800.u4 7800t1 $$[0, 1, 0, 2092, 26688]$$ $$253012016/219375$$ $$-877500000000$$ $$$$ $$9216$$ $$0.97923$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form7800.2.a.u

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} + 4 q^{11} - q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})$$ 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. 