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SageMath
E = EllipticCurve("ea1")
E.isogeny_class()
Elliptic curves in class 102960.ea
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102960.ea1 | 102960bf2 | \([0, 0, 0, -9507, 339986]\) | \(127299503236/6776055\) | \(5058297953280\) | \([2]\) | \(196608\) | \(1.1943\) | |
102960.ea2 | 102960bf1 | \([0, 0, 0, 393, 21206]\) | \(35969456/1061775\) | \(-198152697600\) | \([2]\) | \(98304\) | \(0.84774\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102960.ea have rank \(1\).
Complex multiplication
The elliptic curves in class 102960.ea do not have complex multiplication.Modular form 102960.2.a.ea
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.