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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 37570f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37570.k1 | 37570f1 | \([1, -1, 1, -53953, -4090863]\) | \(719564007681/114920000\) | \(2773889429480000\) | \([2]\) | \(221184\) | \(1.6857\) | \(\Gamma_0(N)\)-optimal |
37570.k2 | 37570f2 | \([1, -1, 1, 96327, -22905919]\) | \(4095232047999/11740625000\) | \(-283390146040625000\) | \([2]\) | \(442368\) | \(2.0323\) |
Rank
sage: E.rank()
The elliptic curves in class 37570f have rank \(0\).
Complex multiplication
The elliptic curves in class 37570f do not have complex multiplication.Modular form 37570.2.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.