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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 152592.cp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152592.cp1 | 152592s3 | \([0, 1, 0, -76733282528, 8181301945441140]\) | \(505384091400037554067434625/815656731648\) | \(80641927743357270884352\) | \([2]\) | \(238878720\) | \(4.5507\) | |
| 152592.cp2 | 152592s4 | \([0, 1, 0, -76732542688, 8181467597688692]\) | \(-505369473241574671219626625/20303219722982711328\) | \(-2007328223173247305673447964672\) | \([2]\) | \(477757440\) | \(4.8973\) | |
| 152592.cp3 | 152592s1 | \([0, 1, 0, -949991648, 11155982031732]\) | \(959024269496848362625/11151660319506432\) | \(1102536582867552454016237568\) | \([2]\) | \(79626240\) | \(4.0014\) | \(\Gamma_0(N)\)-optimal |
| 152592.cp4 | 152592s2 | \([0, 1, 0, -192395488, 28459781364596]\) | \(-7966267523043306625/3534510366354604032\) | \(-349448142229911688356160339968\) | \([2]\) | \(159252480\) | \(4.3480\) |
Rank
sage: E.rank()
The elliptic curves in class 152592.cp have rank \(0\).
Complex multiplication
The elliptic curves in class 152592.cp do not have complex multiplication.Modular form 152592.2.a.cp
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
