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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 63878c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
63878.b2 | 63878c1 | \([1, 1, 0, -26090, 1611724]\) | \(-413493625/152\) | \(-722015844632\) | \([]\) | \(141120\) | \(1.2433\) | \(\Gamma_0(N)\)-optimal |
63878.b3 | 63878c2 | \([1, 1, 0, 15935, 6172277]\) | \(94196375/3511808\) | \(-16681454074377728\) | \([]\) | \(423360\) | \(1.7927\) | |
63878.b1 | 63878c3 | \([1, 1, 0, -143760, -168821504]\) | \(-69173457625/2550136832\) | \(-12113415780813504512\) | \([]\) | \(1270080\) | \(2.3420\) |
Rank
sage: E.rank()
The elliptic curves in class 63878c have rank \(1\).
Complex multiplication
The elliptic curves in class 63878c do not have complex multiplication.Modular form 63878.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.