Properties

 Label 92400dm Number of curves $2$ Conductor $92400$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dm1")

sage: E.isogeny_class()

Elliptic curves in class 92400dm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.v2 92400dm1 $$[0, -1, 0, -533, -14688]$$ $$-67108864/343035$$ $$-85758750000$$ $$[2]$$ $$92160$$ $$0.78222$$ $$\Gamma_0(N)$$-optimal
92400.v1 92400dm2 $$[0, -1, 0, -12908, -559188]$$ $$59466754384/121275$$ $$485100000000$$ $$[2]$$ $$184320$$ $$1.1288$$

Rank

sage: E.rank()

The elliptic curves in class 92400dm have rank $$0$$.

Complex multiplication

The elliptic curves in class 92400dm do not have complex multiplication.

Modular form 92400.2.a.dm

sage: E.q_eigenform(10)

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

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.