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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 762.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
762.f1 | 762g2 | \([1, 0, 0, -22361106, -40701264948]\) | \(1236526859255318155975783969/38367061931916216\) | \(38367061931916216\) | \([]\) | \(25872\) | \(2.6865\) | |
762.f2 | 762g1 | \([1, 0, 0, -101946, 12401892]\) | \(117174888570509216929/1273887851544576\) | \(1273887851544576\) | \([7]\) | \(3696\) | \(1.7135\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 762.f have rank \(0\).
Complex multiplication
The elliptic curves in class 762.f do not have complex multiplication.Modular form 762.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.