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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 76440h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76440.p2 | 76440h1 | \([0, -1, 0, -55133276, 155605284276]\) | \(211072197308055014773168/3052652281946850375\) | \(268047291573189037728000\) | \([2]\) | \(10475520\) | \(3.2993\) | \(\Gamma_0(N)\)-optimal |
| 76440.p1 | 76440h2 | \([0, -1, 0, -107114296, -184496133380]\) | \(386965237776463086681532/182055746334444328125\) | \(63943803896539550256000000\) | \([2]\) | \(20951040\) | \(3.6459\) |
Rank
sage: E.rank()
The elliptic curves in class 76440h have rank \(0\).
Complex multiplication
The elliptic curves in class 76440h do not have complex multiplication.Modular form 76440.2.a.h
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 Cremona 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 Cremona labels.
