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SageMath
E = EllipticCurve("gb1")
E.isogeny_class()
Elliptic curves in class 47040.gb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47040.gb1 | 47040ha2 | \([0, 1, 0, -41225, -2675625]\) | \(16079333824/2953125\) | \(1423082304000000\) | \([2]\) | \(221184\) | \(1.6261\) | |
| 47040.gb2 | 47040ha1 | \([0, 1, 0, 5080, -239982]\) | \(1925134784/4465125\) | \(-33620319432000\) | \([2]\) | \(110592\) | \(1.2795\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 47040.gb have rank \(1\).
Complex multiplication
The elliptic curves in class 47040.gb do not have complex multiplication.Modular form 47040.2.a.gb
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.
