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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 35739.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35739.e1 | 35739i1 | \([1, -1, 1, -405110, 89937244]\) | \(1157625/121\) | \(768526896601470897\) | \([2]\) | \(492480\) | \(2.1669\) | \(\Gamma_0(N)\)-optimal |
| 35739.e2 | 35739i2 | \([1, -1, 1, 520855, 440692786]\) | \(2460375/14641\) | \(-92991754488777978537\) | \([2]\) | \(984960\) | \(2.5135\) |
Rank
sage: E.rank()
The elliptic curves in class 35739.e have rank \(0\).
Complex multiplication
The elliptic curves in class 35739.e do not have complex multiplication.Modular form 35739.2.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.
