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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 64400ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 64400.bd2 | 64400ba1 | \([0, 0, 0, -356075, 110932250]\) | \(-78013216986489/37918720000\) | \(-2426798080000000000\) | \([2]\) | \(774144\) | \(2.2332\) | \(\Gamma_0(N)\)-optimal |
| 64400.bd1 | 64400ba2 | \([0, 0, 0, -6244075, 6004820250]\) | \(420676324562824569/56350000000\) | \(3606400000000000000\) | \([2]\) | \(1548288\) | \(2.5798\) |
Rank
sage: E.rank()
The elliptic curves in class 64400ba have rank \(0\).
Complex multiplication
The elliptic curves in class 64400ba do not have complex multiplication.Modular form 64400.2.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.
