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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 15912.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15912.c1 | 15912q2 | \([0, 0, 0, -471, -934]\) | \(61918288/33813\) | \(6310317312\) | \([2]\) | \(8192\) | \(0.57124\) | |
15912.c2 | 15912q1 | \([0, 0, 0, 114, -115]\) | \(14047232/8619\) | \(-100532016\) | \([2]\) | \(4096\) | \(0.22467\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15912.c have rank \(2\).
Complex multiplication
The elliptic curves in class 15912.c do not have complex multiplication.Modular form 15912.2.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.