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SageMath
E = EllipticCurve("eh1")
E.isogeny_class()
Elliptic curves in class 332010.eh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 332010.eh1 | 332010eh4 | \([1, -1, 1, -4438247, -3177501109]\) | \(13262655736458056369449/1687849747327022580\) | \(1230442465801399460820\) | \([2]\) | \(18350080\) | \(2.7759\) | |
| 332010.eh2 | 332010eh2 | \([1, -1, 1, -1118147, 404222771]\) | \(212076490729573807849/26036036269059600\) | \(18980270440144448400\) | \([2, 2]\) | \(9175040\) | \(2.4293\) | |
| 332010.eh3 | 332010eh1 | \([1, -1, 1, -1082867, 433984979]\) | \(192628775813900462569/3542105790720\) | \(2582195121434880\) | \([4]\) | \(4587520\) | \(2.0827\) | \(\Gamma_0(N)\)-optimal |
| 332010.eh4 | 332010eh3 | \([1, -1, 1, 1637473, 2080741979]\) | \(666068469803369686871/2952087953560672500\) | \(-2152072118145730252500\) | \([2]\) | \(18350080\) | \(2.7759\) |
Rank
sage: E.rank()
The elliptic curves in class 332010.eh have rank \(0\).
Complex multiplication
The elliptic curves in class 332010.eh do not have complex multiplication.Modular form 332010.2.a.eh
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
