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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 147175a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 147175.b2 | 147175a1 | \([0, -1, 1, 35042, -3540182]\) | \(4096/7\) | \(-8132350091796875\) | \([]\) | \(980000\) | \(1.7378\) | \(\Gamma_0(N)\)-optimal |
| 147175.b1 | 147175a2 | \([0, -1, 1, -3118708, 2131548568]\) | \(-2887553024/16807\) | \(-19525772570404296875\) | \([]\) | \(4900000\) | \(2.5426\) |
Rank
sage: E.rank()
The elliptic curves in class 147175a have rank \(0\).
Complex multiplication
The elliptic curves in class 147175a do not have complex multiplication.Modular form 147175.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
