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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 6672.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6672.i1 | 6672h2 | \([0, -1, 0, -13029, 576792]\) | \(-15288691386744832/217535139\) | \(-3480562224\) | \([]\) | \(9792\) | \(0.97053\) | |
6672.i2 | 6672h1 | \([0, -1, 0, -69, 1692]\) | \(-2303721472/73870299\) | \(-1181924784\) | \([]\) | \(3264\) | \(0.42122\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6672.i have rank \(0\).
Complex multiplication
The elliptic curves in class 6672.i do not have complex multiplication.Modular form 6672.2.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.