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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 23805n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23805.h4 | 23805n1 | \([1, -1, 1, 2173297, 775792262]\) | \(10519294081031/8500170375\) | \(-917322772745534925375\) | \([2]\) | \(1267200\) | \(2.7102\) | \(\Gamma_0(N)\)-optimal |
| 23805.h3 | 23805n2 | \([1, -1, 1, -10419548, 6759912206]\) | \(1159246431432649/488076890625\) | \(52672361478536150015625\) | \([2, 2]\) | \(2534400\) | \(3.0568\) | |
| 23805.h2 | 23805n3 | \([1, -1, 1, -78858923, -264834903544]\) | \(502552788401502649/10024505152875\) | \(1081826181894289086007875\) | \([2]\) | \(5068800\) | \(3.4033\) | |
| 23805.h1 | 23805n4 | \([1, -1, 1, -143465693, 661187290232]\) | \(3026030815665395929/1364501953125\) | \(147254544301686767578125\) | \([2]\) | \(5068800\) | \(3.4033\) |
Rank
sage: E.rank()
The elliptic curves in class 23805n have rank \(1\).
Complex multiplication
The elliptic curves in class 23805n do not have complex multiplication.Modular form 23805.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
