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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 26520.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26520.w1 | 26520z4 | \([0, 1, 0, -23576, -1401216]\) | \(1415313160121956/89505\) | \(91653120\) | \([2]\) | \(36864\) | \(0.98770\) | |
26520.w2 | 26520z3 | \([0, 1, 0, -2496, 11280]\) | \(1680085884676/910381875\) | \(932231040000\) | \([2]\) | \(36864\) | \(0.98770\) | |
26520.w3 | 26520z2 | \([0, 1, 0, -1476, -22176]\) | \(1390071129424/10989225\) | \(2813241600\) | \([2, 2]\) | \(18432\) | \(0.64113\) | |
26520.w4 | 26520z1 | \([0, 1, 0, -31, -790]\) | \(-212629504/16286595\) | \(-260585520\) | \([2]\) | \(9216\) | \(0.29455\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 26520.w have rank \(0\).
Complex multiplication
The elliptic curves in class 26520.w do not have complex multiplication.Modular form 26520.2.a.w
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.