Properties

 Label 235200.d Number of curves 2 Conductor 235200 CM no Rank 0 Graph

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Show commands for: SageMath
sage: E = EllipticCurve("235200.d1")

sage: E.isogeny_class()

Elliptic curves in class 235200.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
235200.d1 235200d2 [0, -1, 0, -237813, 44717037] [] 1306368
235200.d2 235200d1 [0, -1, 0, -2613, 76077] [] 435456 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 235200.d have rank $$0$$.

Modular form 235200.2.a.d

sage: E.q_eigenform(10)

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.