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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1078.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1078.c1 | 1078d2 | \([1, 1, 0, -13255, 575933]\) | \(911871625/10648\) | \(3007796451352\) | \([]\) | \(2016\) | \(1.2066\) | |
1078.c2 | 1078d1 | \([1, 1, 0, -1250, -17114]\) | \(765625/22\) | \(6214455478\) | \([]\) | \(672\) | \(0.65732\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1078.c have rank \(0\).
Complex multiplication
The elliptic curves in class 1078.c do not have complex multiplication.Modular form 1078.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.