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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 4928.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4928.w1 | 4928bc2 | \([0, 0, 0, -30028, -2002800]\) | \(11422548526761/4312\) | \(1130364928\) | \([2]\) | \(9216\) | \(1.0877\) | |
| 4928.w2 | 4928bc1 | \([0, 0, 0, -1868, -31600]\) | \(-2749884201/54208\) | \(-14210301952\) | \([2]\) | \(4608\) | \(0.74116\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4928.w have rank \(1\).
Complex multiplication
The elliptic curves in class 4928.w do not have complex multiplication.Modular form 4928.2.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 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.
