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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 11858e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11858.d2 | 11858e1 | \([1, 0, 1, -699746, 225238836]\) | \(73622481625/512\) | \(263513944719872\) | \([3]\) | \(114048\) | \(1.9470\) | \(\Gamma_0(N)\)-optimal |
| 11858.d1 | 11858e2 | \([1, 0, 1, -1025841, -5375548]\) | \(231968823625/134217728\) | \(69078599524646125568\) | \([]\) | \(342144\) | \(2.4963\) |
Rank
sage: E.rank()
The elliptic curves in class 11858e have rank \(0\).
Complex multiplication
The elliptic curves in class 11858e do not have complex multiplication.Modular form 11858.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
