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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 27930.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 27930.u1 | 27930q4 | \([1, 1, 0, -86934747, -312023929419]\) | \(617611911727813844500009/1197723879765000\) | \(140911016730472485000\) | \([2]\) | \(3096576\) | \(3.1196\) | |
| 27930.u2 | 27930q3 | \([1, 1, 0, -14614667, 15174054309]\) | \(2934284984699764805929/851931751022747640\) | \(100228918576075237098360\) | \([2]\) | \(3096576\) | \(3.1196\) | |
| 27930.u3 | 27930q2 | \([1, 1, 0, -5490867, -4768747731]\) | \(155617476551393929129/6633105589454400\) | \(780378239493720705600\) | \([2, 2]\) | \(1548288\) | \(2.7731\) | |
| 27930.u4 | 27930q1 | \([1, 1, 0, 169613, -277722899]\) | \(4586790226340951/286015269335040\) | \(-33649410421998120960\) | \([2]\) | \(774144\) | \(2.4265\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 27930.u have rank \(1\).
Complex multiplication
The elliptic curves in class 27930.u do not have complex multiplication.Modular form 27930.2.a.u
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
