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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 311696f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
311696.f2 | 311696f1 | \([0, 1, 0, -7784, 240436]\) | \(7189057/644\) | \(4673066123264\) | \([2]\) | \(622080\) | \(1.1708\) | \(\Gamma_0(N)\)-optimal |
311696.f1 | 311696f2 | \([0, 1, 0, -27144, -1455500]\) | \(304821217/51842\) | \(376181822922752\) | \([2]\) | \(1244160\) | \(1.5174\) |
Rank
sage: E.rank()
The elliptic curves in class 311696f have rank \(0\).
Complex multiplication
The elliptic curves in class 311696f do not have complex multiplication.Modular form 311696.2.a.f
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.