Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

Elliptic curves in class 64400b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.bc1 64400b1 $$[0, 0, 0, -1175, -14250]$$ $$44851536/4025$$ $$16100000000$$ $$[2]$$ $$30720$$ $$0.69821$$ $$\Gamma_0(N)$$-optimal
64400.bc2 64400b2 $$[0, 0, 0, 1325, -66750]$$ $$16078716/129605$$ $$-2073680000000$$ $$[2]$$ $$61440$$ $$1.0448$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form 64400.2.a.b

sage: E.q_eigenform(10)

$$q - q^{7} - 3q^{9} - 2q^{11} + 4q^{13} - 6q^{17} + O(q^{20})$$

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.