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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 65520.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 65520.f1 | 65520ct3 | \([0, 0, 0, -7272460443, -253158240969142]\) | \(-14245586655234650511684983641/1028175397808386133196800\) | \(-3070115287049476059547513651200\) | \([]\) | \(137168640\) | \(4.5996\) | |
| 65520.f2 | 65520ct1 | \([0, 0, 0, -83296443, 317284097258]\) | \(-21405018343206000779641/2177246093750000000\) | \(-6501222000000000000000000\) | \([]\) | \(15240960\) | \(3.5010\) | \(\Gamma_0(N)\)-optimal |
| 65520.f3 | 65520ct2 | \([0, 0, 0, 512953557, -291028152742]\) | \(4998853083179567995470359/2905108466204672000000\) | \(-8674607398351691317248000000\) | \([]\) | \(45722880\) | \(4.0503\) |
Rank
sage: E.rank()
The elliptic curves in class 65520.f have rank \(0\).
Complex multiplication
The elliptic curves in class 65520.f do not have complex multiplication.Modular form 65520.2.a.f
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
