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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 113288w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
113288.y2 | 113288w1 | \([0, -1, 0, -118008, 11398556]\) | \(62500/17\) | \(49434556968731648\) | \([2]\) | \(884736\) | \(1.9111\) | \(\Gamma_0(N)\)-optimal |
113288.y1 | 113288w2 | \([0, -1, 0, -684448, -208606740]\) | \(6097250/289\) | \(1680774936936876032\) | \([2]\) | \(1769472\) | \(2.2577\) |
Rank
sage: E.rank()
The elliptic curves in class 113288w have rank \(1\).
Complex multiplication
The elliptic curves in class 113288w do not have complex multiplication.Modular form 113288.2.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.