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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 201243.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
201243.c1 | 201243a2 | \([0, 1, 1, -61200232, -184448243696]\) | \(-1713910976512/1594323\) | \(-23581475517717767209707\) | \([]\) | \(28206360\) | \(3.2158\) | |
201243.c2 | 201243a1 | \([0, 1, 1, -156522, 25847924]\) | \(-28672/3\) | \(-44372706504988827\) | \([]\) | \(2169720\) | \(1.9333\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 201243.c have rank \(0\).
Complex multiplication
The elliptic curves in class 201243.c do not have complex multiplication.Modular form 201243.2.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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.