Properties

Label 19800i
Number of curves $2$
Conductor $19800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 19800i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19800.bi1 19800i1 \([0, 0, 0, -8550, 293625]\) \(379275264/15125\) \(2756531250000\) \([2]\) \(36864\) \(1.1536\) \(\Gamma_0(N)\)-optimal
19800.bi2 19800i2 \([0, 0, 0, 3825, 1073250]\) \(2122416/171875\) \(-501187500000000\) \([2]\) \(73728\) \(1.5002\)  

Rank

sage: E.rank()
 

The elliptic curves in class 19800i have rank \(1\).

Complex multiplication

The elliptic curves in class 19800i do not have complex multiplication.

Modular form 19800.2.a.i

sage: E.q_eigenform(10)
 
\(q + 2 q^{7} + q^{11} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.