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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 214774.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
214774.l1 | 214774b2 | \([1, 0, 0, -21032522, -37126217180]\) | \(6950735348004218737/462042447104\) | \(68398864412776115456\) | \([2]\) | \(19464192\) | \(2.8618\) | |
214774.l2 | 214774b1 | \([1, 0, 0, -1396042, -504181980]\) | \(2032601155983217/434808356864\) | \(64367241652991492096\) | \([2]\) | \(9732096\) | \(2.5152\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 214774.l have rank \(0\).
Complex multiplication
The elliptic curves in class 214774.l do not have complex multiplication.Modular form 214774.2.a.l
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.