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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 178024i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 178024.b2 | 178024i1 | \([0, 1, 0, 1106196, 475082080]\) | \(24226243449392/29774625727\) | \(-183983893231267241728\) | \([2]\) | \(4730880\) | \(2.5746\) | \(\Gamma_0(N)\)-optimal |
| 178024.b1 | 178024i2 | \([0, 1, 0, -6586984, 4561699296]\) | \(1278763167594532/375974556419\) | \(9292914480955397540864\) | \([2]\) | \(9461760\) | \(2.9211\) |
Rank
sage: E.rank()
The elliptic curves in class 178024i have rank \(0\).
Complex multiplication
The elliptic curves in class 178024i do not have complex multiplication.Modular form 178024.2.a.i
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.
