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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 342.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
342.b1 | 342f3 | \([1, -1, 0, -787968, 269419360]\) | \(74220219816682217473/16416\) | \(11967264\) | \([2]\) | \(1920\) | \(1.6507\) | |
342.b2 | 342f2 | \([1, -1, 0, -49248, 4218880]\) | \(18120364883707393/269485056\) | \(196454605824\) | \([2, 2]\) | \(960\) | \(1.3042\) | |
342.b3 | 342f4 | \([1, -1, 0, -47808, 4476064]\) | \(-16576888679672833/2216253521952\) | \(-1615648817503008\) | \([2]\) | \(1920\) | \(1.6507\) | |
342.b4 | 342f1 | \([1, -1, 0, -3168, 62464]\) | \(4824238966273/537919488\) | \(392143306752\) | \([2]\) | \(480\) | \(0.95760\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 342.b have rank \(0\).
Complex multiplication
The elliptic curves in class 342.b do not have complex multiplication.Modular form 342.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.