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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 10320c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10320.h3 | 10320c1 | \([0, -1, 0, -76, 160]\) | \(192143824/80625\) | \(20640000\) | \([2]\) | \(3072\) | \(0.10053\) | \(\Gamma_0(N)\)-optimal |
| 10320.h2 | 10320c2 | \([0, -1, 0, -576, -5040]\) | \(20674973956/416025\) | \(426009600\) | \([2, 2]\) | \(6144\) | \(0.44711\) | |
| 10320.h1 | 10320c3 | \([0, -1, 0, -9176, -335280]\) | \(41725476313778/17415\) | \(35665920\) | \([2]\) | \(12288\) | \(0.79368\) | |
| 10320.h4 | 10320c4 | \([0, -1, 0, 24, -15600]\) | \(715822/51282015\) | \(-105025566720\) | \([2]\) | \(12288\) | \(0.79368\) |
Rank
sage: E.rank()
The elliptic curves in class 10320c have rank \(0\).
Complex multiplication
The elliptic curves in class 10320c do not have complex multiplication.Modular form 10320.2.a.c
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.
