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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 18480.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18480.i1 | 18480bq2 | \([0, -1, 0, -13461, 605661]\) | \(-65860951343104/3493875\) | \(-14310912000\) | \([]\) | \(31104\) | \(1.0165\) | |
18480.i2 | 18480bq1 | \([0, -1, 0, -21, 2205]\) | \(-262144/509355\) | \(-2086318080\) | \([]\) | \(10368\) | \(0.46719\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18480.i have rank \(1\).
Complex multiplication
The elliptic curves in class 18480.i do not have complex multiplication.Modular form 18480.2.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.