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SageMath
E = EllipticCurve("jv1")
E.isogeny_class()
Elliptic curves in class 277200.jv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277200.jv1 | 277200jv3 | \([0, 0, 0, -321159348075, 70053359145700250]\) | \(78519570041710065450485106721/96428056919040\) | \(4498947423614730240000000\) | \([4]\) | \(849346560\) | \(4.9046\) | |
277200.jv2 | 277200jv6 | \([0, 0, 0, -94458996075, -10227493675867750]\) | \(1997773216431678333214187041/187585177195046990066400\) | \(8751974027212112368537958400000000\) | \([2]\) | \(1698693120\) | \(5.2512\) | |
277200.jv3 | 277200jv4 | \([0, 0, 0, -20975796075, 990672085732250]\) | \(21876183941534093095979041/3572502915711058560000\) | \(166678696035415148175360000000000\) | \([2, 2]\) | \(849346560\) | \(4.9046\) | |
277200.jv4 | 277200jv2 | \([0, 0, 0, -20072628075, 1094564403940250]\) | \(19170300594578891358373921/671785075055001600\) | \(31342804461766154649600000000\) | \([2, 2]\) | \(424673280\) | \(4.5580\) | |
277200.jv5 | 277200jv1 | \([0, 0, 0, -1198260075, 18706553572250]\) | \(-4078208988807294650401/880065599546327040\) | \(-41060340612433434378240000000\) | \([2]\) | \(212336640\) | \(4.2115\) | \(\Gamma_0(N)\)-optimal |
277200.jv6 | 277200jv5 | \([0, 0, 0, 38056715925, 5559729482020250]\) | \(130650216943167617311657439/361816948816603087500000\) | \(-16880931563987433650400000000000000\) | \([2]\) | \(1698693120\) | \(5.2512\) |
Rank
sage: E.rank()
The elliptic curves in class 277200.jv have rank \(0\).
Complex multiplication
The elliptic curves in class 277200.jv do not have complex multiplication.Modular form 277200.2.a.jv
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.