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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 25152.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25152.c1 | 25152bb1 | \([0, -1, 0, -4545, 118881]\) | \(39616946929/226368\) | \(59341012992\) | \([2]\) | \(55296\) | \(0.90869\) | \(\Gamma_0(N)\)-optimal |
25152.c2 | 25152bb2 | \([0, -1, 0, -1985, 249441]\) | \(-3301293169/100082952\) | \(-26236145369088\) | \([2]\) | \(110592\) | \(1.2553\) |
Rank
sage: E.rank()
The elliptic curves in class 25152.c have rank \(0\).
Complex multiplication
The elliptic curves in class 25152.c do not have complex multiplication.Modular form 25152.2.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.