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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 9522.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9522.i1 | 9522k2 | \([1, -1, 1, -150071, 22396281]\) | \(3463512697/3174\) | \(342532249619094\) | \([2]\) | \(67584\) | \(1.7125\) | |
9522.i2 | 9522k1 | \([1, -1, 1, -7241, 514725]\) | \(-389017/828\) | \(-89356239031068\) | \([2]\) | \(33792\) | \(1.3659\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9522.i have rank \(0\).
Complex multiplication
The elliptic curves in class 9522.i do not have complex multiplication.Modular form 9522.2.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.