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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 53900.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53900.ba1 | 53900h1 | \([0, 1, 0, -377708, -89766412]\) | \(-20261200/77\) | \(-22647432500000000\) | \([]\) | \(414720\) | \(1.9974\) | \(\Gamma_0(N)\)-optimal |
| 53900.ba2 | 53900h2 | \([0, 1, 0, 847292, -469516412]\) | \(228714800/456533\) | \(-134276627292500000000\) | \([]\) | \(1244160\) | \(2.5467\) |
Rank
sage: E.rank()
The elliptic curves in class 53900.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 53900.ba do not have complex multiplication.Modular form 53900.2.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.
