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SageMath
E = EllipticCurve("dr1")
E.isogeny_class()
Elliptic curves in class 87360.dr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87360.dr1 | 87360fq4 | \([0, -1, 0, -99905, 12187617]\) | \(841356017734178/1404585\) | \(184101765120\) | \([4]\) | \(327680\) | \(1.4237\) | |
| 87360.dr2 | 87360fq3 | \([0, -1, 0, -16385, -551775]\) | \(3711757787138/1124589375\) | \(147402178560000\) | \([2]\) | \(327680\) | \(1.4237\) | |
| 87360.dr3 | 87360fq2 | \([0, -1, 0, -6305, 188097]\) | \(423026849956/16769025\) | \(1098974822400\) | \([2, 2]\) | \(163840\) | \(1.0772\) | |
| 87360.dr4 | 87360fq1 | \([0, -1, 0, 175, 10545]\) | \(35969456/2985255\) | \(-48910417920\) | \([2]\) | \(81920\) | \(0.73060\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 87360.dr have rank \(1\).
Complex multiplication
The elliptic curves in class 87360.dr do not have complex multiplication.Modular form 87360.2.a.dr
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
