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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 2850.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2850.h1 | 2850l4 | \([1, 0, 1, -12312001, 16627013648]\) | \(13209596798923694545921/92340\) | \(1442812500\) | \([2]\) | \(92160\) | \(2.2922\) | |
| 2850.h2 | 2850l3 | \([1, 0, 1, -779001, 253003648]\) | \(3345930611358906241/165622259047500\) | \(2587847797617187500\) | \([2]\) | \(92160\) | \(2.2922\) | |
| 2850.h3 | 2850l2 | \([1, 0, 1, -769501, 259748648]\) | \(3225005357698077121/8526675600\) | \(133229306250000\) | \([2, 2]\) | \(46080\) | \(1.9456\) | |
| 2850.h4 | 2850l1 | \([1, 0, 1, -47501, 4160648]\) | \(-758575480593601/40535043840\) | \(-633360060000000\) | \([2]\) | \(23040\) | \(1.5991\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2850.h have rank \(1\).
Complex multiplication
The elliptic curves in class 2850.h do not have complex multiplication.Modular form 2850.2.a.h
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.
