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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 29575.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29575.i1 | 29575q2 | \([1, 1, 1, -70223, 1998706]\) | \(63473450669/33787663\) | \(20385824482170875\) | \([2]\) | \(225792\) | \(1.8208\) | |
29575.i2 | 29575q1 | \([1, 1, 1, -40648, -3147344]\) | \(12310389629/107653\) | \(64952558659625\) | \([2]\) | \(112896\) | \(1.4743\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29575.i have rank \(0\).
Complex multiplication
The elliptic curves in class 29575.i do not have complex multiplication.Modular form 29575.2.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.