Properties

 Label 2240w Number of curves $3$ Conductor $2240$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("w1")

sage: E.isogeny_class()

Elliptic curves in class 2240w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2240.u2 2240w1 $$[0, 1, 0, -5, -7]$$ $$-262144/35$$ $$-2240$$ $$[]$$ $$96$$ $$-0.62458$$ $$\Gamma_0(N)$$-optimal
2240.u3 2240w2 $$[0, 1, 0, 35, 25]$$ $$71991296/42875$$ $$-2744000$$ $$[]$$ $$288$$ $$-0.075270$$
2240.u1 2240w3 $$[0, 1, 0, -525, 4673]$$ $$-250523582464/13671875$$ $$-875000000$$ $$[]$$ $$864$$ $$0.47404$$

Rank

sage: E.rank()

The elliptic curves in class 2240w have rank $$1$$.

Complex multiplication

The elliptic curves in class 2240w do not have complex multiplication.

Modular form2240.2.a.w

sage: E.q_eigenform(10)

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

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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.