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SageMath
E = EllipticCurve("ek1")
E.isogeny_class()
Elliptic curves in class 159600.ek
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 159600.ek1 | 159600cb4 | \([0, 1, 0, -35575008, -78827856012]\) | \(77799851782095807001/3092322318750000\) | \(197908628400000000000000\) | \([2]\) | \(14155776\) | \(3.2368\) | |
| 159600.ek2 | 159600cb2 | \([0, 1, 0, -5783008, 3695983988]\) | \(334199035754662681/101099003040000\) | \(6470336194560000000000\) | \([2, 2]\) | \(7077888\) | \(2.8902\) | |
| 159600.ek3 | 159600cb1 | \([0, 1, 0, -5271008, 4655471988]\) | \(253060782505556761/41184460800\) | \(2635805491200000000\) | \([2]\) | \(3538944\) | \(2.5437\) | \(\Gamma_0(N)\)-optimal |
| 159600.ek4 | 159600cb3 | \([0, 1, 0, 15816992, 24820783988]\) | \(6837784281928633319/8113766016106800\) | \(-519281025030835200000000\) | \([2]\) | \(14155776\) | \(3.2368\) |
Rank
sage: E.rank()
The elliptic curves in class 159600.ek have rank \(0\).
Complex multiplication
The elliptic curves in class 159600.ek do not have complex multiplication.Modular form 159600.2.a.ek
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
