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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 3120i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3120.v2 | 3120i1 | \([0, 1, 0, 720, 8100]\) | \(40254822716/49359375\) | \(-50544000000\) | \([2]\) | \(1920\) | \(0.73996\) | \(\Gamma_0(N)\)-optimal |
3120.v1 | 3120i2 | \([0, 1, 0, -4280, 74100]\) | \(4234737878642/1247410125\) | \(2554695936000\) | \([2]\) | \(3840\) | \(1.0865\) |
Rank
sage: E.rank()
The elliptic curves in class 3120i have rank \(1\).
Complex multiplication
The elliptic curves in class 3120i do not have complex multiplication.Modular form 3120.2.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.