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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 316239.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
316239.c1 | 316239c2 | \([1, 1, 1, -42847428173, 3389952595320110]\) | \(3390686569246875224955063625/27273014317398421790757\) | \(69975093087184238963466307001613\) | \([2]\) | \(970776576\) | \(4.9378\) | |
316239.c2 | 316239c1 | \([1, 1, 1, -894334188, 122427479679588]\) | \(-30832792962533430765625/2505834498623945462127\) | \(-6429285749702731031954953211943\) | \([2]\) | \(485388288\) | \(4.5912\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 316239.c have rank \(0\).
Complex multiplication
The elliptic curves in class 316239.c do not have complex multiplication.Modular form 316239.2.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.