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SageMath
E = EllipticCurve("dq1")
E.isogeny_class()
Elliptic curves in class 135240.dq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
135240.dq1 | 135240ck2 | \([0, 1, 0, -1188840, 433184688]\) | \(264527137402013054/37471584403125\) | \(26322439066156800000\) | \([2]\) | \(3317760\) | \(2.4523\) | |
135240.dq2 | 135240ck1 | \([0, 1, 0, -313840, -61015312]\) | \(9733205763526108/1069365234375\) | \(375595290000000000\) | \([2]\) | \(1658880\) | \(2.1057\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 135240.dq have rank \(0\).
Complex multiplication
The elliptic curves in class 135240.dq do not have complex multiplication.Modular form 135240.2.a.dq
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.