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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 361920.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
361920.f1 | 361920f2 | \([0, -1, 0, -9081, -315495]\) | \(20221464942784/1001766285\) | \(4103234703360\) | \([2]\) | \(933888\) | \(1.1793\) | |
361920.f2 | 361920f1 | \([0, -1, 0, 344, -19550]\) | \(70138418624/2590301025\) | \(-165779265600\) | \([2]\) | \(466944\) | \(0.83273\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 361920.f have rank \(2\).
Complex multiplication
The elliptic curves in class 361920.f do not have complex multiplication.Modular form 361920.2.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.