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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 2310.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2310.o1 | 2310o4 | \([1, 1, 1, -89210930, 324283935935]\) | \(78519570041710065450485106721/96428056919040\) | \(96428056919040\) | \([4]\) | \(184320\) | \(2.8574\) | |
| 2310.o2 | 2310o5 | \([1, 1, 1, -26238610, -47360440513]\) | \(1997773216431678333214187041/187585177195046990066400\) | \(187585177195046990066400\) | \([2]\) | \(368640\) | \(3.2040\) | |
| 2310.o3 | 2310o3 | \([1, 1, 1, -5826610, 4584017087]\) | \(21876183941534093095979041/3572502915711058560000\) | \(3572502915711058560000\) | \([2, 2]\) | \(184320\) | \(2.8574\) | |
| 2310.o4 | 2310o2 | \([1, 1, 1, -5575730, 5065104575]\) | \(19170300594578891358373921/671785075055001600\) | \(671785075055001600\) | \([2, 4]\) | \(92160\) | \(2.5109\) | |
| 2310.o5 | 2310o1 | \([1, 1, 1, -332850, 86465727]\) | \(-4078208988807294650401/880065599546327040\) | \(-880065599546327040\) | \([4]\) | \(46080\) | \(2.1643\) | \(\Gamma_0(N)\)-optimal |
| 2310.o6 | 2310o6 | \([1, 1, 1, 10571310, 25743893055]\) | \(130650216943167617311657439/361816948816603087500000\) | \(-361816948816603087500000\) | \([2]\) | \(368640\) | \(3.2040\) |
Rank
sage: E.rank()
The elliptic curves in class 2310.o have rank \(0\).
Complex multiplication
The elliptic curves in class 2310.o do not have complex multiplication.Modular form 2310.2.a.o
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
