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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 11858.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11858.r1 | 11858o2 | \([1, 1, 0, -50266185, 1793546693]\) | \(231968823625/134217728\) | \(8127028155475092026949632\) | \([]\) | \(2395008\) | \(3.4692\) | |
| 11858.r2 | 11858o1 | \([1, 1, 0, -34287530, -77291208364]\) | \(73622481625/512\) | \(31002152082348220928\) | \([]\) | \(798336\) | \(2.9199\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11858.r have rank \(1\).
Complex multiplication
The elliptic curves in class 11858.r do not have complex multiplication.Modular form 11858.2.a.r
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
