Properties

 Label 19800.e Number of curves 4 Conductor 19800 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("19800.e1")

sage: E.isogeny_class()

Elliptic curves in class 19800.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19800.e1 19800n3 [0, 0, 0, -158475, -24282250] [2] 98304
19800.e2 19800n4 [0, 0, 0, -23475, 854750] [2] 98304
19800.e3 19800n2 [0, 0, 0, -9975, -373750] [2, 2] 49152
19800.e4 19800n1 [0, 0, 0, 150, -19375] [2] 24576 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 19800.e have rank $$1$$.

Modular form 19800.2.a.e

sage: E.q_eigenform(10)

$$q - 4q^{7} + q^{11} - 6q^{13} + 6q^{17} - 8q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.