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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 26928by
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26928.m3 | 26928by1 | \([0, 0, 0, -1192251, -450858134]\) | \(62768149033310713/6915442583808\) | \(20649400908169347072\) | \([2]\) | \(737280\) | \(2.4396\) | \(\Gamma_0(N)\)-optimal |
| 26928.m2 | 26928by2 | \([0, 0, 0, -4521531, 3217342570]\) | \(3423676911662954233/483711578981136\) | \(1444355035452408397824\) | \([2, 2]\) | \(1474560\) | \(2.7861\) | |
| 26928.m4 | 26928by3 | \([0, 0, 0, 7375749, 17291824810]\) | \(14861225463775641287/51859390496937804\) | \(-154851310273608331739136\) | \([4]\) | \(2949120\) | \(3.1327\) | |
| 26928.m1 | 26928by4 | \([0, 0, 0, -69687291, 223907705386]\) | \(12534210458299016895673/315581882565708\) | \(942322452031083036672\) | \([2]\) | \(2949120\) | \(3.1327\) |
Rank
sage: E.rank()
The elliptic curves in class 26928by have rank \(1\).
Complex multiplication
The elliptic curves in class 26928by do not have complex multiplication.Modular form 26928.2.a.by
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.
