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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 152460.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152460.c1 | 152460y2 | \([0, 0, 0, -107396635863, -13513282233118162]\) | \(414354576760345737269208016/1182266314178222109375\) | \(390875923350749289376109340000000\) | \([2]\) | \(838656000\) | \(5.1253\) | |
152460.c2 | 152460y1 | \([0, 0, 0, -4026713988, -381725555696287]\) | \(-349439858058052607328256/2844147488104248046875\) | \(-58770006079975118165917968750000\) | \([2]\) | \(419328000\) | \(4.7787\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 152460.c have rank \(0\).
Complex multiplication
The elliptic curves in class 152460.c do not have complex multiplication.Modular form 152460.2.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.