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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 40733.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40733.g1 | 40733a1 | \([0, 1, 1, -47257, -3969915]\) | \(-78843215872/539\) | \(-79791344171\) | \([]\) | \(83160\) | \(1.2727\) | \(\Gamma_0(N)\)-optimal |
| 40733.g2 | 40733a2 | \([0, 1, 1, -26097, -7511570]\) | \(-13278380032/156590819\) | \(-23181061099903091\) | \([]\) | \(249480\) | \(1.8221\) | |
| 40733.g3 | 40733a3 | \([0, 1, 1, 233113, 194283415]\) | \(9463555063808/115539436859\) | \(-17103983249981432651\) | \([]\) | \(748440\) | \(2.3714\) |
Rank
sage: E.rank()
The elliptic curves in class 40733.g have rank \(1\).
Complex multiplication
The elliptic curves in class 40733.g do not have complex multiplication.Modular form 40733.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
