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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 187850ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
187850.h2 | 187850ba1 | \([1, 0, 1, -37721, -3568452]\) | \(-9836106385/3407872\) | \(-2056443638579200\) | \([]\) | \(1814400\) | \(1.6497\) | \(\Gamma_0(N)\)-optimal |
187850.h1 | 187850ba2 | \([1, 0, 1, -3274521, -2280980932]\) | \(-6434774386429585/140608\) | \(-84848382548800\) | \([]\) | \(5443200\) | \(2.1990\) |
Rank
sage: E.rank()
The elliptic curves in class 187850ba have rank \(1\).
Complex multiplication
The elliptic curves in class 187850ba do not have complex multiplication.Modular form 187850.2.a.ba
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.