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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 3840.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3840.b1 | 3840q2 | \([0, -1, 0, -23661, 1407861]\) | \(44708635815488/34171875\) | \(1119744000000\) | \([2]\) | \(10752\) | \(1.2442\) | |
| 3840.b2 | 3840q1 | \([0, -1, 0, -1791, 12555]\) | \(1241603628992/597871125\) | \(306110016000\) | \([2]\) | \(5376\) | \(0.89763\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3840.b have rank \(0\).
Complex multiplication
The elliptic curves in class 3840.b do not have complex multiplication.Modular form 3840.2.a.b
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.
