Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 274890.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
274890.c1 | 274890c4 | \([1, 1, 0, -120413703, -508561492347]\) | \(1641206446466677841336041/268339886718750000\) | \(31569919332574218750000\) | \([2]\) | \(47185920\) | \(3.3260\) | |
274890.c2 | 274890c2 | \([1, 1, 0, -8258583, -6308433963]\) | \(529483179157097938921/160443506916000000\) | \(18876018145160484000000\) | \([2, 2]\) | \(23592960\) | \(2.9794\) | |
274890.c3 | 274890c1 | \([1, 1, 0, -3178263, 2103559893]\) | \(30179023393892020201/1196047835136000\) | \(140713831755915264000\) | \([2]\) | \(11796480\) | \(2.6328\) | \(\Gamma_0(N)\)-optimal |
274890.c4 | 274890c3 | \([1, 1, 0, 22611417, -42321375963]\) | \(10867228028544202381079/12868640151403806000\) | \(-1513982645172506372094000\) | \([2]\) | \(47185920\) | \(3.3260\) |
Rank
sage: E.rank()
The elliptic curves in class 274890.c have rank \(0\).
Complex multiplication
The elliptic curves in class 274890.c do not have complex multiplication.Modular form 274890.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.