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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 102960.dc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.dc1 | 102960em2 | \([0, 0, 0, -2323114707, -43097699921006]\) | \(464352938845529653759213009/2445173327025000\) | \(7301248431723417600000\) | \([2]\) | \(30965760\) | \(3.8119\) | |
| 102960.dc2 | 102960em1 | \([0, 0, 0, -145114707, -674180321006]\) | \(-113180217375258301213009/260161419375000000\) | \(-776837835671040000000000\) | \([2]\) | \(15482880\) | \(3.4654\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102960.dc have rank \(1\).
Complex multiplication
The elliptic curves in class 102960.dc do not have complex multiplication.Modular form 102960.2.a.dc
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
