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SageMath
E = EllipticCurve("jg1")
E.isogeny_class()
Elliptic curves in class 142800.jg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 142800.jg1 | 142800bz4 | \([0, 1, 0, -337558408, -2384892716812]\) | \(66464620505913166201729/74880071980801920\) | \(4792324606771322880000000\) | \([2]\) | \(41287680\) | \(3.6496\) | |
| 142800.jg2 | 142800bz3 | \([0, 1, 0, -239766408, 1416818899188]\) | \(23818189767728437646209/232359312482640000\) | \(14870995998888960000000000\) | \([2]\) | \(41287680\) | \(3.6496\) | |
| 142800.jg3 | 142800bz2 | \([0, 1, 0, -26518408, -16634156812]\) | \(32224493437735955329/16782725759385600\) | \(1074094448600678400000000\) | \([2, 2]\) | \(20643840\) | \(3.3030\) | |
| 142800.jg4 | 142800bz1 | \([0, 1, 0, 6249592, -2019628812]\) | \(421792317902132351/271682182840320\) | \(-17387659701780480000000\) | \([2]\) | \(10321920\) | \(2.9564\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 142800.jg have rank \(0\).
Complex multiplication
The elliptic curves in class 142800.jg do not have complex multiplication.Modular form 142800.2.a.jg
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.
