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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 67032.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67032.v1 | 67032ch4 | \([0, 0, 0, -261435531, 1627027786006]\) | \(22501000029889239268/3620708343\) | \(317986928487882243072\) | \([2]\) | \(9437184\) | \(3.3364\) | |
67032.v2 | 67032ch2 | \([0, 0, 0, -16389471, 25259710210]\) | \(22174957026242512/278654127129\) | \(6118165397630770331904\) | \([2, 2]\) | \(4718592\) | \(2.9898\) | |
67032.v3 | 67032ch3 | \([0, 0, 0, -2815491, 65832336430]\) | \(-28104147578308/21301741002339\) | \(-1870814921028882387987456\) | \([2]\) | \(9437184\) | \(3.3364\) | |
67032.v4 | 67032ch1 | \([0, 0, 0, -1922466, -401863259]\) | \(572616640141312/280535480757\) | \(384967039798368537552\) | \([2]\) | \(2359296\) | \(2.6433\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 67032.v have rank \(0\).
Complex multiplication
The elliptic curves in class 67032.v do not have complex multiplication.Modular form 67032.2.a.v
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.