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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 203280h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.gz5 | 203280h1 | \([0, 1, 0, -644397640, 7377095661428]\) | \(-4078208988807294650401/880065599546327040\) | \(-6386032204176960214259466240\) | \([2]\) | \(132710400\) | \(4.0564\) | \(\Gamma_0(N)\)-optimal |
| 203280.gz4 | 203280h2 | \([0, 1, 0, -10794613320, 431660171171700]\) | \(19170300594578891358373921/671785075055001600\) | \(4874683348375608072182169600\) | \([2, 2]\) | \(265420800\) | \(4.4030\) | |
| 203280.gz1 | 203280h3 | \([0, 1, 0, -172712360520, 27626911621191540]\) | \(78519570041710065450485106721/96428056919040\) | \(699712245528786622218240\) | \([2]\) | \(530841600\) | \(4.7495\) | |
| 203280.gz3 | 203280h4 | \([0, 1, 0, -11280317000, 390687957260148]\) | \(21876183941534093095979041/3572502915711058560000\) | \(25923202407874554321355407360000\) | \([2, 2]\) | \(530841600\) | \(4.7495\) | |
| 203280.gz6 | 203280h5 | \([0, 1, 0, 20466056120, 2192599397002100]\) | \(130650216943167617311657439/361816948816603087500000\) | \(-2625457339033559786678630400000000\) | \([2]\) | \(1061683200\) | \(5.0961\) | |
| 203280.gz2 | 203280h6 | \([0, 1, 0, -50797949000, -4033437401562252]\) | \(1997773216431678333214187041/187585177195046990066400\) | \(1361176920460634688589912680038400\) | \([2]\) | \(1061683200\) | \(5.0961\) |
Rank
sage: E.rank()
The elliptic curves in class 203280h have rank \(0\).
Complex multiplication
The elliptic curves in class 203280h do not have complex multiplication.Modular form 203280.2.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 Cremona numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
