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SageMath
E = EllipticCurve("ih1")
E.isogeny_class()
Elliptic curves in class 152880.ih
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152880.ih1 | 152880bi4 | \([0, 1, 0, -259464787080, -31621772317509900]\) | \(4008766897254067912673785886329/1423480510711669921875000000\) | \(685961456044921875000000000000000000\) | \([2]\) | \(1981808640\) | \(5.5774\) | |
| 152880.ih2 | 152880bi2 | \([0, 1, 0, -109676632200, 13620182067183348]\) | \(302773487204995438715379645049/8911747415025000000000000\) | \(4294484670997611417600000000000000\) | \([2, 2]\) | \(990904320\) | \(5.2308\) | |
| 152880.ih3 | 152880bi1 | \([0, 1, 0, -108889872520, 13830181128634100]\) | \(296304326013275547793071733369/268420373544960000000\) | \(129349175407374332067840000000\) | \([2]\) | \(495452160\) | \(4.8843\) | \(\Gamma_0(N)\)-optimal |
| 152880.ih4 | 152880bi3 | \([0, 1, 0, 27523367800, 45422209107183348]\) | \(4784981304203817469820354951/1852343836482910078035000000\) | \(-892626534475275828308949872640000000\) | \([4]\) | \(1981808640\) | \(5.5774\) |
Rank
sage: E.rank()
The elliptic curves in class 152880.ih have rank \(0\).
Complex multiplication
The elliptic curves in class 152880.ih do not have complex multiplication.Modular form 152880.2.a.ih
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.
