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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 11495f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11495.b3 | 11495f1 | \([1, -1, 1, -118871512, 498873762786]\) | \(104857852278310619039721/47155625\) | \(83539066180625\) | \([4]\) | \(529920\) | \(2.9148\) | \(\Gamma_0(N)\)-optimal |
11495.b2 | 11495f2 | \([1, -1, 1, -118872117, 498868431284]\) | \(104859453317683374662841/2223652969140625\) | \(3939336877663734765625\) | \([2, 2]\) | \(1059840\) | \(3.2613\) | |
11495.b1 | 11495f3 | \([1, -1, 1, -123031492, 462086246284]\) | \(116256292809537371612841/15216540068579856875\) | \(26957028940433399825331875\) | \([2]\) | \(2119680\) | \(3.6079\) | |
11495.b4 | 11495f4 | \([1, -1, 1, -114722422, 535309392896]\) | \(-94256762600623910012361/15323275604248046875\) | \(-27146117452737274169921875\) | \([2]\) | \(2119680\) | \(3.6079\) |
Rank
sage: E.rank()
The elliptic curves in class 11495f have rank \(1\).
Complex multiplication
The elliptic curves in class 11495f do not have complex multiplication.Modular form 11495.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.