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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 26950.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26950.g1 | 26950o4 | \([1, 0, 1, -4312026, 3427268198]\) | \(4823468134087681/30382271150\) | \(55850684664474218750\) | \([2]\) | \(1327104\) | \(2.6265\) | |
| 26950.g2 | 26950o2 | \([1, 0, 1, -330776, -70106802]\) | \(2177286259681/105875000\) | \(194626373046875000\) | \([2]\) | \(442368\) | \(2.0772\) | |
| 26950.g3 | 26950o3 | \([1, 0, 1, -110276, 116289198]\) | \(-80677568161/3131816380\) | \(-5757110395165937500\) | \([2]\) | \(663552\) | \(2.2799\) | |
| 26950.g4 | 26950o1 | \([1, 0, 1, 12224, -4250802]\) | \(109902239/4312000\) | \(-7926601375000000\) | \([2]\) | \(221184\) | \(1.7306\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 26950.g have rank \(0\).
Complex multiplication
The elliptic curves in class 26950.g do not have complex multiplication.Modular form 26950.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
