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SageMath
E = EllipticCurve("pv1")
E.isogeny_class()
Elliptic curves in class 176400.pv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.pv1 | 176400cf4 | \([0, 0, 0, -5842515, -5417907950]\) | \(502270291349/1889568\) | \(82975189875572736000\) | \([2]\) | \(5529600\) | \(2.6814\) | |
| 176400.pv2 | 176400cf2 | \([0, 0, 0, -374115, 88065250]\) | \(131872229/18\) | \(790420571136000\) | \([2]\) | \(1105920\) | \(1.8767\) | |
| 176400.pv3 | 176400cf3 | \([0, 0, 0, -197715, -162599150]\) | \(-19465109/248832\) | \(-10926773975384064000\) | \([2]\) | \(2764800\) | \(2.3349\) | |
| 176400.pv4 | 176400cf1 | \([0, 0, 0, -21315, 1629250]\) | \(-24389/12\) | \(-526947047424000\) | \([2]\) | \(552960\) | \(1.5301\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 176400.pv have rank \(1\).
Complex multiplication
The elliptic curves in class 176400.pv do not have complex multiplication.Modular form 176400.2.a.pv
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.
\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
