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SageMath
E = EllipticCurve("if1")
E.isogeny_class()
Elliptic curves in class 162240.if
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162240.if1 | 162240t2 | \([0, 1, 0, -2305, 33983]\) | \(18821096/3645\) | \(262408273920\) | \([2]\) | \(258048\) | \(0.90810\) | |
162240.if2 | 162240t1 | \([0, 1, 0, 295, 3303]\) | \(314432/675\) | \(-6074265600\) | \([2]\) | \(129024\) | \(0.56153\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 162240.if have rank \(1\).
Complex multiplication
The elliptic curves in class 162240.if do not have complex multiplication.Modular form 162240.2.a.if
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.