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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 185150p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
185150.bz2 | 185150p1 | \([1, -1, 1, -108280, -63802153]\) | \(-60698457/725788\) | \(-1678791746961437500\) | \([2]\) | \(3244032\) | \(2.1789\) | \(\Gamma_0(N)\)-optimal |
185150.bz1 | 185150p2 | \([1, -1, 1, -3150030, -2144359153]\) | \(1494447319737/5411854\) | \(12517947156690718750\) | \([2]\) | \(6488064\) | \(2.5255\) |
Rank
sage: E.rank()
The elliptic curves in class 185150p have rank \(0\).
Complex multiplication
The elliptic curves in class 185150p do not have complex multiplication.Modular form 185150.2.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 Cremona 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 Cremona labels.