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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 44880.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44880.r1 | 44880bh4 | \([0, -1, 0, -1351776, -604479744]\) | \(66692696957462376289/1322972640\) | \(5418895933440\) | \([2]\) | \(491520\) | \(1.9758\) | |
| 44880.r2 | 44880bh3 | \([0, -1, 0, -128096, 1355520]\) | \(56751044592329569/32660264340000\) | \(133776442736640000\) | \([2]\) | \(491520\) | \(1.9758\) | |
| 44880.r3 | 44880bh2 | \([0, -1, 0, -84576, -9402624]\) | \(16334668434139489/72511718400\) | \(297007998566400\) | \([2, 2]\) | \(245760\) | \(1.6293\) | |
| 44880.r4 | 44880bh1 | \([0, -1, 0, -2656, -293120]\) | \(-506071034209/8823767040\) | \(-36142149795840\) | \([2]\) | \(122880\) | \(1.2827\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 44880.r have rank \(1\).
Complex multiplication
The elliptic curves in class 44880.r do not have complex multiplication.Modular form 44880.2.a.r
sage: E.q_eigenform(10)
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.
