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SageMath
E = EllipticCurve("ep1")
E.isogeny_class()
Elliptic curves in class 152880.ep
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152880.ep1 | 152880gi2 | \([0, 1, 0, -107114296, 184496133380]\) | \(386965237776463086681532/182055746334444328125\) | \(63943803896539550256000000\) | \([2]\) | \(41902080\) | \(3.6459\) | |
152880.ep2 | 152880gi1 | \([0, 1, 0, -55133276, -155605284276]\) | \(211072197308055014773168/3052652281946850375\) | \(268047291573189037728000\) | \([2]\) | \(20951040\) | \(3.2993\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 152880.ep have rank \(1\).
Complex multiplication
The elliptic curves in class 152880.ep do not have complex multiplication.Modular form 152880.2.a.ep
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.