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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 12480.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12480.i1 | 12480bw2 | \([0, -1, 0, -161, -159]\) | \(14172488/7605\) | \(249200640\) | \([2]\) | \(3072\) | \(0.30233\) | |
12480.i2 | 12480bw1 | \([0, -1, 0, 39, -39]\) | \(1560896/975\) | \(-3993600\) | \([2]\) | \(1536\) | \(-0.044240\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 12480.i have rank \(1\).
Complex multiplication
The elliptic curves in class 12480.i do not have complex multiplication.Modular form 12480.2.a.i
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.