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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 348480.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
348480.p1 | 348480p1 | \([0, 0, 0, -11543763, -15092411312]\) | \(1546408574144/455625\) | \(50124403154109240000\) | \([2]\) | \(16220160\) | \(2.7590\) | \(\Gamma_0(N)\)-optimal |
348480.p2 | 348480p2 | \([0, 0, 0, -10046388, -19150896512]\) | \(-15926924096/13286025\) | \(-93544166142324828057600\) | \([2]\) | \(32440320\) | \(3.1056\) |
Rank
sage: E.rank()
The elliptic curves in class 348480.p have rank \(1\).
Complex multiplication
The elliptic curves in class 348480.p do not have complex multiplication.Modular form 348480.2.a.p
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.