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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 28611w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28611.z3 | 28611w1 | \([0, 0, 1, -867, -23337]\) | \(-4096/11\) | \(-193559165811\) | \([]\) | \(30720\) | \(0.85318\) | \(\Gamma_0(N)\)-optimal |
28611.z2 | 28611w2 | \([0, 0, 1, -26877, 3071853]\) | \(-122023936/161051\) | \(-2833899746638851\) | \([]\) | \(153600\) | \(1.6579\) | |
28611.z1 | 28611w3 | \([0, 0, 1, -20340687, 35309904183]\) | \(-52893159101157376/11\) | \(-193559165811\) | \([]\) | \(768000\) | \(2.4626\) |
Rank
sage: E.rank()
The elliptic curves in class 28611w have rank \(1\).
Complex multiplication
The elliptic curves in class 28611w do not have complex multiplication.Modular form 28611.2.a.w
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.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.