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SageMath
E = EllipticCurve("kr1")
E.isogeny_class()
Elliptic curves in class 277200kr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277200.kr2 | 277200kr1 | \([0, 0, 0, -1458075, 1058386250]\) | \(-7347774183121/6119866368\) | \(-285528485265408000000\) | \([2]\) | \(10321920\) | \(2.6229\) | \(\Gamma_0(N)\)-optimal |
| 277200.kr1 | 277200kr2 | \([0, 0, 0, -26802075, 53393746250]\) | \(45637459887836881/13417633152\) | \(626013092339712000000\) | \([2]\) | \(20643840\) | \(2.9695\) |
Rank
sage: E.rank()
The elliptic curves in class 277200kr have rank \(0\).
Complex multiplication
The elliptic curves in class 277200kr do not have complex multiplication.Modular form 277200.2.a.kr
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
