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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 126960.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
126960.i1 | 126960bh2 | \([0, -1, 0, -9376701, 11017708785]\) | \(4547904200704/17578125\) | \(352399433764500000000\) | \([]\) | \(5723136\) | \(2.8008\) | |
126960.i2 | 126960bh1 | \([0, -1, 0, -616461, -174373839]\) | \(1292345344/91125\) | \(1826838664635168000\) | \([]\) | \(1907712\) | \(2.2515\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 126960.i have rank \(1\).
Complex multiplication
The elliptic curves in class 126960.i do not have complex multiplication.Modular form 126960.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.