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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 363090cj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 363090.cj4 | 363090cj1 | \([1, 0, 1, -15351089, -21642646588]\) | \(3400580030216483633401/248179914178560000\) | \(29198118723193405440000\) | \([2]\) | \(42467328\) | \(3.0570\) | \(\Gamma_0(N)\)-optimal |
| 363090.cj2 | 363090cj2 | \([1, 0, 1, -241143089, -1441332425788]\) | \(13181351126943641326385401/78687520727961600\) | \(9257508126123954278400\) | \([2, 2]\) | \(84934656\) | \(3.4035\) | |
| 363090.cj3 | 363090cj3 | \([1, 0, 1, -236674289, -1497319339708]\) | \(-12462027714326806804452601/1020321931394362309440\) | \(-120039854906615331343306560\) | \([2]\) | \(169869312\) | \(3.7501\) | |
| 363090.cj1 | 363090cj4 | \([1, 0, 1, -3858283889, -92244588212668]\) | \(53990582156643221755293310201/1924038392640\) | \(226361192855703360\) | \([2]\) | \(169869312\) | \(3.7501\) |
Rank
sage: E.rank()
The elliptic curves in class 363090cj have rank \(1\).
Complex multiplication
The elliptic curves in class 363090cj do not have complex multiplication.Modular form 363090.2.a.cj
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
