Properties

 Label 242550md Number of curves 4 Conductor 242550 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("242550.md1")

sage: E.isogeny_class()

Elliptic curves in class 242550md

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
242550.md3 242550md1 [1, -1, 1, -617630, 3635869997] [2] 15925248 $$\Gamma_0(N)$$-optimal
242550.md2 242550md2 [1, -1, 1, -39425630, 94446589997] [2] 31850496
242550.md4 242550md3 [1, -1, 1, 5556370, -97938778003] [2] 47775744
242550.md1 242550md4 [1, -1, 1, -287929130, -1827155344003] [2] 95551488

Rank

sage: E.rank()

The elliptic curves in class 242550md have rank $$1$$.

Modular form 242550.2.a.md

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{8} + q^{11} - 4q^{13} + q^{16} + 4q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.