Properties

 Label 62400a Number of curves $4$ Conductor $62400$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

Elliptic curves in class 62400a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.cp3 62400a1 $$[0, -1, 0, -6508, 204262]$$ $$30488290624/195$$ $$195000000$$ $$$$ $$36864$$ $$0.77535$$ $$\Gamma_0(N)$$-optimal
62400.cp2 62400a2 $$[0, -1, 0, -6633, 196137]$$ $$504358336/38025$$ $$2433600000000$$ $$[2, 2]$$ $$73728$$ $$1.1219$$
62400.cp4 62400a3 $$[0, -1, 0, 6367, 859137]$$ $$55742968/658125$$ $$-336960000000000$$ $$$$ $$147456$$ $$1.4685$$
62400.cp1 62400a4 $$[0, -1, 0, -21633, -988863]$$ $$2186875592/428415$$ $$219348480000000$$ $$$$ $$147456$$ $$1.4685$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form 62400.2.a.a

sage: E.q_eigenform(10)

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