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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 26928.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26928.o1 | 26928bn4 | \([0, 0, 0, -26211, -1627486]\) | \(666940371553/2756193\) | \(8229948198912\) | \([2]\) | \(65536\) | \(1.3335\) | |
| 26928.o2 | 26928bn2 | \([0, 0, 0, -2451, 2450]\) | \(545338513/314721\) | \(939751870464\) | \([2, 2]\) | \(32768\) | \(0.98694\) | |
| 26928.o3 | 26928bn1 | \([0, 0, 0, -1731, 27650]\) | \(192100033/561\) | \(1675137024\) | \([2]\) | \(16384\) | \(0.64036\) | \(\Gamma_0(N)\)-optimal |
| 26928.o4 | 26928bn3 | \([0, 0, 0, 9789, 19586]\) | \(34741712447/20160657\) | \(-60199399231488\) | \([2]\) | \(65536\) | \(1.3335\) |
Rank
sage: E.rank()
The elliptic curves in class 26928.o have rank \(2\).
Complex multiplication
The elliptic curves in class 26928.o do not have complex multiplication.Modular form 26928.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
