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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 303450.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
303450.p1 | 303450p2 | \([1, 1, 0, -3274066700, -72122050446000]\) | \(-4928752745352265/1056964608\) | \(-832357110436901683200000000\) | \([]\) | \(317260800\) | \(4.1605\) | |
303450.p2 | 303450p1 | \([1, 1, 0, 14572675, -340918807875]\) | \(434602535/64012032\) | \(-50409322682557110300000000\) | \([]\) | \(105753600\) | \(3.6112\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 303450.p have rank \(0\).
Complex multiplication
The elliptic curves in class 303450.p do not have complex multiplication.Modular form 303450.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.