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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 152592k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152592.cc4 | 152592k1 | \([0, 1, 0, -27036624, 42305909652]\) | \(22106889268753393/4969545596928\) | \(491326462953454747779072\) | \([2]\) | \(18579456\) | \(3.2589\) | \(\Gamma_0(N)\)-optimal |
| 152592.cc2 | 152592k2 | \([0, 1, 0, -405834704, 3146480415636]\) | \(74768347616680342513/5615307472896\) | \(555171314004962630959104\) | \([2, 2]\) | \(37158912\) | \(3.6054\) | |
| 152592.cc1 | 152592k3 | \([0, 1, 0, -6493238224, 201388863447956]\) | \(306234591284035366263793/1727485056\) | \(170792098757299666944\) | \([4]\) | \(74317824\) | \(3.9520\) | |
| 152592.cc3 | 152592k4 | \([0, 1, 0, -379200464, 3577326535572]\) | \(-60992553706117024753/20624795251201152\) | \(-2039121586121687610488782848\) | \([2]\) | \(74317824\) | \(3.9520\) |
Rank
sage: E.rank()
The elliptic curves in class 152592k have rank \(1\).
Complex multiplication
The elliptic curves in class 152592k do not have complex multiplication.Modular form 152592.2.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 Cremona 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 Cremona labels.
