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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 259920.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
259920.w1 | 259920w2 | \([0, 0, 0, -900120288, -10394388364048]\) | \(1590409933520896/45\) | \(2282069137653780480\) | \([]\) | \(42550272\) | \(3.4832\) | |
259920.w2 | 259920w1 | \([0, 0, 0, -11193888, -14039220688]\) | \(3058794496/91125\) | \(4621190003748905472000\) | \([]\) | \(14183424\) | \(2.9339\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 259920.w have rank \(1\).
Complex multiplication
The elliptic curves in class 259920.w do not have complex multiplication.Modular form 259920.2.a.w
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.