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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 350658ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350658.ba2 | 350658ba1 | \([1, -1, 0, 37548, 13163728]\) | \(4533086375/60669952\) | \(-78353299688767488\) | \([2]\) | \(3440640\) | \(1.9224\) | \(\Gamma_0(N)\)-optimal |
| 350658.ba1 | 350658ba2 | \([1, -1, 0, -659412, 193118800]\) | \(24553362849625/1755162752\) | \(2266736474589890688\) | \([2]\) | \(6881280\) | \(2.2690\) |
Rank
sage: E.rank()
The elliptic curves in class 350658ba have rank \(0\).
Complex multiplication
The elliptic curves in class 350658ba do not have complex multiplication.Modular form 350658.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
