Properties

 Label 2496.d Number of curves $2$ Conductor $2496$ CM no Rank $0$ Graph Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 2496.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2496.d1 2496f2 $$[0, -1, 0, -11609, -477447]$$ $$42246001231552/14414517$$ $$59041861632$$ $$$$ $$3072$$ $$1.0384$$
2496.d2 2496f1 $$[0, -1, 0, -624, -9486]$$ $$-420526439488/390971529$$ $$-25022177856$$ $$$$ $$1536$$ $$0.69180$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 2496.d have rank $$0$$.

Complex multiplication

The elliptic curves in class 2496.d do not have complex multiplication.

Modular form2496.2.a.d

sage: E.q_eigenform(10)

$$q - q^{3} - 2 q^{5} + 2 q^{7} + q^{9} + 2 q^{11} + q^{13} + 2 q^{15} + 6 q^{17} - 2 q^{19} + O(q^{20})$$ 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 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. 