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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 6498.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6498.f1 | 6498j3 | \([1, -1, 0, -277857, -453398531]\) | \(-69173457625/2550136832\) | \(-87460633336419975168\) | \([]\) | \(194400\) | \(2.5067\) | |
| 6498.f2 | 6498j1 | \([1, -1, 0, -50427, 4372573]\) | \(-413493625/152\) | \(-5213059981848\) | \([]\) | \(21600\) | \(1.4081\) | \(\Gamma_0(N)\)-optimal |
| 6498.f3 | 6498j2 | \([1, -1, 0, 30798, 16559572]\) | \(94196375/3511808\) | \(-120442537820616192\) | \([]\) | \(64800\) | \(1.9574\) |
Rank
sage: E.rank()
The elliptic curves in class 6498.f have rank \(1\).
Complex multiplication
The elliptic curves in class 6498.f do not have complex multiplication.Modular form 6498.2.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.
