Properties

 Label 78897.d Number of curves $2$ Conductor $78897$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

Elliptic curves in class 78897.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
78897.d1 78897b1 $$[1, 1, 1, -131501, 18289946]$$ $$10418796526321/6390657$$ $$154254924292833$$ $$[2]$$ $$645120$$ $$1.6653$$ $$\Gamma_0(N)$$-optimal
78897.d2 78897b2 $$[1, 1, 1, -106936, 25364666]$$ $$-5602762882081/8312741073$$ $$-200649361228671537$$ $$[2]$$ $$1290240$$ $$2.0118$$

Rank

sage: E.rank()

The elliptic curves in class 78897.d have rank $$0$$.

Complex multiplication

The elliptic curves in class 78897.d do not have complex multiplication.

Modular form 78897.2.a.d

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} - q^{4} + 4q^{5} + q^{6} - q^{7} + 3q^{8} + q^{9} - 4q^{10} + 4q^{11} + q^{12} + q^{13} + q^{14} - 4q^{15} - q^{16} - q^{18} + O(q^{20})$$

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.