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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 395c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
395.a1 | 395c1 | \([0, -1, 1, -50, 156]\) | \(-14102327296/246875\) | \(-246875\) | \([5]\) | \(68\) | \(-0.16783\) | \(\Gamma_0(N)\)-optimal |
395.a2 | 395c2 | \([0, -1, 1, 300, -5724]\) | \(2976041775104/15385281995\) | \(-15385281995\) | \([]\) | \(340\) | \(0.63689\) |
Rank
sage: E.rank()
The elliptic curves in class 395c have rank \(0\).
Complex multiplication
The elliptic curves in class 395c do not have complex multiplication.Modular form 395.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.