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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 3744.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3744.i1 | 3744m2 | \([0, 0, 0, -11820, 494336]\) | \(61162984000/41067\) | \(122625404928\) | \([2]\) | \(5120\) | \(1.0661\) | |
| 3744.i2 | 3744m1 | \([0, 0, 0, -885, 4448]\) | \(1643032000/767637\) | \(35814871872\) | \([2]\) | \(2560\) | \(0.71954\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3744.i have rank \(0\).
Complex multiplication
The elliptic curves in class 3744.i do not have complex multiplication.Modular form 3744.2.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 LMFDB 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 LMFDB labels.
