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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 55506.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
55506.c1 | 55506l2 | \([1, 1, 0, -29895044, -63107695536]\) | \(-4967448100211756593/16591334871936\) | \(-9868912908348081219456\) | \([]\) | \(7620480\) | \(3.0850\) | |
55506.c2 | 55506l1 | \([1, 1, 0, 784636, -449131824]\) | \(89813071796687/198690471936\) | \(-118185726368028819456\) | \([]\) | \(2540160\) | \(2.5357\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 55506.c have rank \(0\).
Complex multiplication
The elliptic curves in class 55506.c do not have complex multiplication.Modular form 55506.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.