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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 94640.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
94640.f1 | 94640e2 | \([0, 1, 0, -142016, -1215980]\) | \(32044133522/18484375\) | \(182723681504000000\) | \([2]\) | \(1032192\) | \(2.0018\) | |
94640.f2 | 94640e1 | \([0, 1, 0, -94696, 11144004]\) | \(19000416964/79625\) | \(393558698624000\) | \([2]\) | \(516096\) | \(1.6552\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 94640.f have rank \(1\).
Complex multiplication
The elliptic curves in class 94640.f do not have complex multiplication.Modular form 94640.2.a.f
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.