Properties

 Label 64400e Number of curves $2$ Conductor $64400$ CM no Rank $1$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

Elliptic curves in class 64400e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.d1 64400e1 $$[0, 1, 0, -1008, -2012]$$ $$7086244/4025$$ $$64400000000$$ $$[2]$$ $$49152$$ $$0.76392$$ $$\Gamma_0(N)$$-optimal
64400.d2 64400e2 $$[0, 1, 0, 3992, -12012]$$ $$219804478/129605$$ $$-4147360000000$$ $$[2]$$ $$98304$$ $$1.1105$$

Rank

sage: E.rank()

The elliptic curves in class 64400e have rank $$1$$.

Complex multiplication

The elliptic curves in class 64400e do not have complex multiplication.

Modular form 64400.2.a.e

sage: E.q_eigenform(10)

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.