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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 26928.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 26928.k1 | 26928p4 | \([0, 0, 0, -57891, 5357234]\) | \(28742820444292/24805737\) | \(18517383447552\) | \([4]\) | \(73728\) | \(1.4722\) | |
| 26928.k2 | 26928p3 | \([0, 0, 0, -38091, -2831254]\) | \(8187726931492/99379467\) | \(74186374597632\) | \([2]\) | \(73728\) | \(1.4722\) | |
| 26928.k3 | 26928p2 | \([0, 0, 0, -4431, 43310]\) | \(51553893328/25492401\) | \(4757493844224\) | \([2, 2]\) | \(36864\) | \(1.1256\) | |
| 26928.k4 | 26928p1 | \([0, 0, 0, 1014, 5195]\) | \(9885304832/6720219\) | \(-78384634416\) | \([2]\) | \(18432\) | \(0.77907\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 26928.k have rank \(1\).
Complex multiplication
The elliptic curves in class 26928.k do not have complex multiplication.Modular form 26928.2.a.k
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.
