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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 1078.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1078.l1 | 1078l2 | \([1, 1, 1, -57, 41]\) | \(59776471/29282\) | \(10043726\) | \([2]\) | \(256\) | \(0.036835\) | |
1078.l2 | 1078l1 | \([1, 1, 1, 13, 13]\) | \(704969/484\) | \(-166012\) | \([2]\) | \(128\) | \(-0.30974\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1078.l have rank \(0\).
Complex multiplication
The elliptic curves in class 1078.l do not have complex multiplication.Modular form 1078.2.a.l
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.