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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 330330.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 330330.e1 | 330330e1 | \([1, 1, 0, -53748, 3490128]\) | \(12901648554332819/3461770690560\) | \(4607616789135360\) | \([2]\) | \(2903040\) | \(1.7138\) | \(\Gamma_0(N)\)-optimal |
| 330330.e2 | 330330e2 | \([1, 1, 0, 136332, 22840272]\) | \(210539747068814701/290318954889600\) | \(-386414528958057600\) | \([2]\) | \(5806080\) | \(2.0603\) |
Rank
sage: E.rank()
The elliptic curves in class 330330.e have rank \(0\).
Complex multiplication
The elliptic curves in class 330330.e do not have complex multiplication.Modular form 330330.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
