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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 74704.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 74704.b1 | 74704k2 | \([0, 1, 0, -2769778264, -56107736647404]\) | \(573718392227901342193352375257/22016176259779893044\) | \(90178257960058441908224\) | \([2]\) | \(34922496\) | \(3.8957\) | |
| 74704.b2 | 74704k1 | \([0, 1, 0, -172853784, -879463116140]\) | \(-139444195316122186685933977/867810592237096964848\) | \(-3554552185803149168017408\) | \([2]\) | \(17461248\) | \(3.5491\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 74704.b have rank \(1\).
Complex multiplication
The elliptic curves in class 74704.b do not have complex multiplication.Modular form 74704.2.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.
