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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 254100w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254100.w1 | 254100w1 | \([0, -1, 0, -16133, -284238]\) | \(1048576/525\) | \(232517381250000\) | \([2]\) | \(806400\) | \(1.4495\) | \(\Gamma_0(N)\)-optimal |
| 254100.w2 | 254100w2 | \([0, -1, 0, 59492, -2250488]\) | \(3286064/2205\) | \(-15625168020000000\) | \([2]\) | \(1612800\) | \(1.7960\) |
Rank
sage: E.rank()
The elliptic curves in class 254100w have rank \(1\).
Complex multiplication
The elliptic curves in class 254100w do not have complex multiplication.Modular form 254100.2.a.w
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
