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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 478800.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
478800.ba1 | 478800ba3 | \([0, 0, 0, -133385475, 592940155250]\) | \(22501000029889239268/3620708343\) | \(42231942112752000000\) | \([2]\) | \(50331648\) | \(3.1682\) | \(\Gamma_0(N)\)-optimal* |
478800.ba2 | 478800ba2 | \([0, 0, 0, -8361975, 9205433750]\) | \(22174957026242512/278654127129\) | \(812555434708164000000\) | \([2, 2]\) | \(25165824\) | \(2.8216\) | \(\Gamma_0(N)\)-optimal* |
478800.ba3 | 478800ba4 | \([0, 0, 0, -1436475, 23991376250]\) | \(-28104147578308/21301741002339\) | \(-248463507051282096000000\) | \([2]\) | \(50331648\) | \(3.1682\) | |
478800.ba4 | 478800ba1 | \([0, 0, 0, -980850, -146451625]\) | \(572616640141312/280535480757\) | \(51127591367963250000\) | \([2]\) | \(12582912\) | \(2.4750\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 478800.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 478800.ba do not have complex multiplication.Modular form 478800.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.