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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 232760w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
232760.w1 | 232760w1 | \([0, 0, 0, -20102, 1058529]\) | \(379275264/15125\) | \(35824685138000\) | \([2]\) | \(540672\) | \(1.3673\) | \(\Gamma_0(N)\)-optimal |
232760.w2 | 232760w2 | \([0, 0, 0, 8993, 3869106]\) | \(2122416/171875\) | \(-6513579116000000\) | \([2]\) | \(1081344\) | \(1.7139\) |
Rank
sage: E.rank()
The elliptic curves in class 232760w have rank \(0\).
Complex multiplication
The elliptic curves in class 232760w do not have complex multiplication.Modular form 232760.2.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 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.