Properties

Label 100800.r
Number of curves $4$
Conductor $100800$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100800.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100800.r1 100800mi4 \([0, 0, 0, -91854000300, -10715075262502000]\) \(229625675762164624948320008/9568125\) \(3571283520000000000\) \([2]\) \(165150720\) \(4.4606\)  
100800.r2 100800mi2 \([0, 0, 0, -5740875300, -167423033752000]\) \(448487713888272974160064/91549016015625\) \(4271310891225000000000000\) \([2, 2]\) \(82575360\) \(4.1140\)  
100800.r3 100800mi3 \([0, 0, 0, -5721192300, -168628066378000]\) \(-55486311952875723077768/801237030029296875\) \(-299060118984375000000000000000\) \([2]\) \(165150720\) \(4.4606\)  
100800.r4 100800mi1 \([0, 0, 0, -360035175, -2597139043000]\) \(7079962908642659949376/100085966990454375\) \(72962669936041239375000000\) \([2]\) \(41287680\) \(3.7674\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 100800.r have rank \(1\).

Complex multiplication

The elliptic curves in class 100800.r do not have complex multiplication.

Modular form 100800.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{7} - 4q^{11} - 6q^{13} + 6q^{17} + 4q^{19} + O(q^{20})\)  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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.