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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 12274b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12274.d2 | 12274b1 | \([1, -1, 0, -146453, -21472139]\) | \(7384117376817/25137152\) | \(1182599461670912\) | \([2]\) | \(69120\) | \(1.7559\) | \(\Gamma_0(N)\)-optimal |
| 12274.d1 | 12274b2 | \([1, -1, 0, -2341333, -1378346955]\) | \(30171143454741297/351424\) | \(16533051684544\) | \([2]\) | \(138240\) | \(2.1025\) |
Rank
sage: E.rank()
The elliptic curves in class 12274b have rank \(0\).
Complex multiplication
The elliptic curves in class 12274b do not have complex multiplication.Modular form 12274.2.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 Cremona 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 Cremona labels.
