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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 97020.cx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
97020.cx1 | 97020cx2 | \([0, 0, 0, -11487, -641914]\) | \(-18330740176/8857805\) | \(-81000871015680\) | \([]\) | \(311040\) | \(1.3744\) | |
97020.cx2 | 97020cx1 | \([0, 0, 0, 1113, 10766]\) | \(16674224/15125\) | \(-138311712000\) | \([]\) | \(103680\) | \(0.82507\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 97020.cx have rank \(0\).
Complex multiplication
The elliptic curves in class 97020.cx do not have complex multiplication.Modular form 97020.2.a.cx
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.