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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 825.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
825.c1 | 825c1 | \([0, 1, 1, -583, 5494]\) | \(-56197120/3267\) | \(-1276171875\) | \([3]\) | \(360\) | \(0.50351\) | \(\Gamma_0(N)\)-optimal |
825.c2 | 825c2 | \([0, 1, 1, 3167, 11119]\) | \(8990228480/5314683\) | \(-2076048046875\) | \([]\) | \(1080\) | \(1.0528\) |
Rank
sage: E.rank()
The elliptic curves in class 825.c have rank \(1\).
Complex multiplication
The elliptic curves in class 825.c do not have complex multiplication.Modular form 825.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.