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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 262080.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
262080.e1 | 262080e1 | \([0, 0, 0, -19525068, -30560756112]\) | \(4307585705106105969/381542350192640\) | \(72913878591847677296640\) | \([2]\) | \(32440320\) | \(3.1271\) | \(\Gamma_0(N)\)-optimal |
262080.e2 | 262080e2 | \([0, 0, 0, 21762612, -142582489488]\) | \(5964709808210123151/49408483478681600\) | \(-9442108232422886316441600\) | \([2]\) | \(64880640\) | \(3.4737\) |
Rank
sage: E.rank()
The elliptic curves in class 262080.e have rank \(0\).
Complex multiplication
The elliptic curves in class 262080.e do not have complex multiplication.Modular form 262080.2.a.e
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.