Properties

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

Show commands: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

Elliptic curves in class 7800.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7800.n1 7800u3 $$[0, 1, 0, -7608, -251712]$$ $$3044193988/85293$$ $$1364688000000$$ $$$$ $$16384$$ $$1.1076$$
7800.n2 7800u2 $$[0, 1, 0, -1108, 8288]$$ $$37642192/13689$$ $$54756000000$$ $$[2, 2]$$ $$8192$$ $$0.76098$$
7800.n3 7800u1 $$[0, 1, 0, -983, 11538]$$ $$420616192/117$$ $$29250000$$ $$$$ $$4096$$ $$0.41441$$ $$\Gamma_0(N)$$-optimal
7800.n4 7800u4 $$[0, 1, 0, 3392, 62288]$$ $$269676572/257049$$ $$-4112784000000$$ $$$$ $$16384$$ $$1.1076$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form7800.2.a.n

sage: E.q_eigenform(10)

$$q + q^{3} - 4 q^{7} + q^{9} - q^{13} - 2 q^{17} + 8 q^{19} + O(q^{20})$$ 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels. 