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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 100022.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100022.c1 | 100022c2 | \([1, 1, 0, -474, -3700]\) | \(11816519211433/1539138536\) | \(1539138536\) | \([2]\) | \(82272\) | \(0.49125\) | |
100022.c2 | 100022c1 | \([1, 1, 0, 46, -268]\) | \(10403062487/41609152\) | \(-41609152\) | \([2]\) | \(41136\) | \(0.14467\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 100022.c have rank \(1\).
Complex multiplication
The elliptic curves in class 100022.c do not have complex multiplication.Modular form 100022.2.a.c
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.