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SageMath
E = EllipticCurve("ep1")
E.isogeny_class()
Elliptic curves in class 254016.ep
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254016.ep1 | 254016ep4 | \([0, 0, 0, -30402540, 64522794672]\) | \(-189613868625/128\) | \(-2097940603273740288\) | \([]\) | \(8709120\) | \(2.8313\) | |
| 254016.ep2 | 254016ep3 | \([0, 0, 0, -296940, 126514864]\) | \(-1159088625/2097152\) | \(-5238935961596854272\) | \([]\) | \(2903040\) | \(2.2820\) | |
| 254016.ep3 | 254016ep1 | \([0, 0, 0, -14700, -718928]\) | \(-140625/8\) | \(-19984954687488\) | \([]\) | \(414720\) | \(1.3091\) | \(\Gamma_0(N)\)-optimal |
| 254016.ep4 | 254016ep2 | \([0, 0, 0, 79380, -1333584]\) | \(3375/2\) | \(-32780321926152192\) | \([]\) | \(1244160\) | \(1.8584\) |
Rank
sage: E.rank()
The elliptic curves in class 254016.ep have rank \(0\).
Complex multiplication
The elliptic curves in class 254016.ep do not have complex multiplication.Modular form 254016.2.a.ep
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 21 & 7 \\ 3 & 1 & 7 & 21 \\ 21 & 7 & 1 & 3 \\ 7 & 21 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
