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SageMath
E = EllipticCurve("en1")
E.isogeny_class()
Elliptic curves in class 76050.en
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76050.en1 | 76050eh3 | \([1, -1, 1, -17473280, 28117549347]\) | \(-10730978619193/6656\) | \(-365949351144000000\) | \([]\) | \(3265920\) | \(2.6909\) | |
| 76050.en2 | 76050eh2 | \([1, -1, 1, -171905, 54719097]\) | \(-10218313/17576\) | \(-966335005364625000\) | \([]\) | \(1088640\) | \(2.1416\) | |
| 76050.en3 | 76050eh1 | \([1, -1, 1, 18220, -1557903]\) | \(12167/26\) | \(-1429489652906250\) | \([]\) | \(362880\) | \(1.5923\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 76050.en have rank \(1\).
Complex multiplication
The elliptic curves in class 76050.en do not have complex multiplication.Modular form 76050.2.a.en
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
