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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 26928.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26928.z1 | 26928br3 | \([0, 0, 0, -2389617795, -44961498702718]\) | \(505384091400037554067434625/815656731648\) | \(2435537950193221632\) | \([2]\) | \(6635520\) | \(3.6834\) | |
| 26928.z2 | 26928br4 | \([0, 0, 0, -2389594755, -44962409063806]\) | \(-505369473241574671219626625/20303219722982711328\) | \(-60625089241310808302026752\) | \([2]\) | \(13271040\) | \(4.0300\) | |
| 26928.z3 | 26928br1 | \([0, 0, 0, -29584515, -61310821246]\) | \(959024269496848362625/11151660319506432\) | \(33298679287481093849088\) | \([2]\) | \(2211840\) | \(3.1341\) | \(\Gamma_0(N)\)-optimal |
| 26928.z4 | 26928br2 | \([0, 0, 0, -5991555, -156404605822]\) | \(-7966267523043306625/3534510366354604032\) | \(-10553991401768985965887488\) | \([2]\) | \(4423680\) | \(3.4807\) |
Rank
sage: E.rank()
The elliptic curves in class 26928.z have rank \(1\).
Complex multiplication
The elliptic curves in class 26928.z do not have complex multiplication.Modular form 26928.2.a.z
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
