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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 12880.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12880.e1 | 12880x1 | \([0, -1, 0, -2632810, -1643408833]\) | \(-126142795384287538429696/9315359375\) | \(-149045750000\) | \([]\) | \(141696\) | \(2.0402\) | \(\Gamma_0(N)\)-optimal |
12880.e2 | 12880x2 | \([0, -1, 0, -2606310, -1678138133]\) | \(-122372013839654770813696/5297595236711512175\) | \(-84761523787384194800\) | \([]\) | \(425088\) | \(2.5895\) |
Rank
sage: E.rank()
The elliptic curves in class 12880.e have rank \(0\).
Complex multiplication
The elliptic curves in class 12880.e do not have complex multiplication.Modular form 12880.2.a.e
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.