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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 18515n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18515.h4 | 18515n1 | \([1, -1, 1, 1223, -28676024]\) | \(1367631/2399636575\) | \(-355232333657040175\) | \([2]\) | \(190080\) | \(2.0465\) | \(\Gamma_0(N)\)-optimal |
18515.h3 | 18515n2 | \([1, -1, 1, -1397982, -625297036]\) | \(2041085246738049/38897700625\) | \(5758255692077730625\) | \([2, 2]\) | \(380160\) | \(2.3931\) | |
18515.h1 | 18515n3 | \([1, -1, 1, -22264387, -40430051214]\) | \(8244966675515989329/3081640625\) | \(456193409500390625\) | \([2]\) | \(760320\) | \(2.7397\) | |
18515.h2 | 18515n4 | \([1, -1, 1, -2918857, 978921914]\) | \(18577831198352049/7958740140575\) | \(1178179172030005096175\) | \([4]\) | \(760320\) | \(2.7397\) |
Rank
sage: E.rank()
The elliptic curves in class 18515n have rank \(0\).
Complex multiplication
The elliptic curves in class 18515n do not have complex multiplication.Modular form 18515.2.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.