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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 325.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
325.c1 | 325a2 | \([0, 1, 1, -1333, -19131]\) | \(671088640/2197\) | \(858203125\) | \([]\) | \(180\) | \(0.57960\) | |
325.c2 | 325a1 | \([0, 1, 1, -83, 244]\) | \(163840/13\) | \(5078125\) | \([3]\) | \(60\) | \(0.030295\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 325.c have rank \(1\).
Complex multiplication
The elliptic curves in class 325.c do not have complex multiplication.Modular form 325.2.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.