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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 37440.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37440.ba1 | 37440c1 | \([0, 0, 0, -168, 842]\) | \(-303464448/1625\) | \(-2808000\) | \([]\) | \(6912\) | \(0.081859\) | \(\Gamma_0(N)\)-optimal |
37440.ba2 | 37440c2 | \([0, 0, 0, 432, 4482]\) | \(7077888/10985\) | \(-13837936320\) | \([]\) | \(20736\) | \(0.63117\) |
Rank
sage: E.rank()
The elliptic curves in class 37440.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 37440.ba do not have complex multiplication.Modular form 37440.2.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 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.