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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 480240.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
480240.f1 | 480240f2 | \([0, 0, 0, -16193163, -25080444038]\) | \(157264717208387436361/4368589453125\) | \(13044538209600000000\) | \([2]\) | \(33816576\) | \(2.7707\) | \(\Gamma_0(N)\)-optimal* |
480240.f2 | 480240f1 | \([0, 0, 0, -971643, -424625942]\) | \(-33974761330806841/6424789539375\) | \(-19184318767941120000\) | \([2]\) | \(16908288\) | \(2.4241\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 480240.f have rank \(1\).
Complex multiplication
The elliptic curves in class 480240.f do not have complex multiplication.Modular form 480240.2.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 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.