Properties

 Label 62400.p Number of curves $2$ Conductor $62400$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("p1")

sage: E.isogeny_class()

Elliptic curves in class 62400.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.p1 62400fr2 $$[0, -1, 0, -24833, -482463]$$ $$26463592/13689$$ $$876096000000000$$ $$[2]$$ $$286720$$ $$1.5592$$
62400.p2 62400fr1 $$[0, -1, 0, -19833, -1067463]$$ $$107850176/117$$ $$936000000000$$ $$[2]$$ $$143360$$ $$1.2127$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 62400.p have rank $$1$$.

Complex multiplication

The elliptic curves in class 62400.p do not have complex multiplication.

Modular form 62400.2.a.p

sage: E.q_eigenform(10)

$$q - q^{3} - 4q^{7} + q^{9} + 2q^{11} - q^{13} - 2q^{19} + O(q^{20})$$

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.